A nice pure Top X list here much like the counterspells one. It would be easy enough to work this out from my ratings however here it is for convenience sake. It is far far easier to compare a narrow style of card like counterspells or burn directly, especially given their colour confinements as they all do the same one thing. Without further-a-do here is my list:
10. Lava Dart 1 (4)
9. Seal of Fire 4 (8)
8. Searing Blaze 2 (18)
7. Searing Spear 4.5
6. Incinerate 4.5
5. Chain Lightening 9
4. Burst Lightening 4 (3.6)
3. Fireblast 2.6 (20)
2. Arc Trail 9
1. Lightening Bolt 9
Ball Lightening 12
Galvanic Blast 16
I imagine many are wondering where Lightening Helix is on my list and will be assuming I have excluded non-red cards or something similar however I just don't think it is top 10 material. It is the most overrated burn spell going as it is hard to cast and is at somewhat cross purposes. Certainly it is a card that offers huge value and is well above the curve on power but life schmife is all I can say. In a control deck it is a decent tempo card as the life is significant but in the agro decks the simple Incinerate is so much more forgiving on your mana and does exactly the same thing, if not more, for you. I hate gold cards anyway for their lack of playability and stand by my rating of Seal of Fire and Lava Dart above it. To be fair to the card the only other burn spell not on this list I might rate above it is Firebolt and so the very worst Helix is would be the 12th best burn spell.
Another exclusion which deserves honourable mention is Galvanic Blast which is quite significantly better than all the other burn when in the right deck. Burn is very simple to break down into a numerical comparison where you factor in the burn per mana and burn per card. By doing this you can get an all round value score for your card which accounts for both forms of card efficiency. Obviously you will tend to favour mana efficiency or damage efficiency on your burn depending on what kind of deck you are building so the scoring isn't all that relevant beyond a theoretical point of view. More significant are the factors that fall outside the considerations of these efficiencies such as prerequisites for the effects or additional costs or stipulations. Fireblast would technically score infinite due to not costing mana to use most of the time. It is hard to simply mathematically compare saccing two lands to a normal mana cost and my method of removing infinities is somewhat of a botch. The numbers by the sides of the card are suppost to represent the combined score of mana efficiency and burn efficiency, Lightning Bolt is 3 burn for one mana and one card, 3 x 3 = 9, simple.
Galvanic Blast gets a near top score when it is cast with metal craft and has all the benefits that the rating does not account for as well being both one mana and instants speed. Despite this there are not enough artifact decks that really want good cheap burn to merit it having a main cube slot.
Lightning Bolt is a clear winner, the score system doesn't account for instant speed which is always nice. Nine is a good score although not the highest, it gets the top spot for being so consistently good. One mana spells are a premium and with no drawback or downside Bolt goes in every red deck very happily.
Arc Trail gets a more controversial second place. In cube there are far greater numbers of cheap spells than other formats and lots of small utility creatures to boot. Arc Trail is very easy to get a two for one with and can even find it happening against non agro decks. It is at its strongest against the agro decks where it can so easily take all the steam out of their draw. In these situations where you cast it on turn two or three and hit two dorks it is about the best tempo card in the cube. It also offers cheap card advantage in red where it is short supply. The worst it ever is still makes it playable in decks like red deck wins where you want all your cards to be able to do two damage to the dome. The score for Arc Trail can be 2 at worst when it is two mana and a card for just two damage but when you get the two for one it is a high scorer as well.
Fireblast is the narrowest of the burn spells in this list but it is also the most powerful by quite some way. When you can afford so sac two mountains the score is equivalent to 20 which is over double the number one card! When you can't however it is a pathetic 2.6 which is fairly unplayable thus illustrating why the card is narrow - unless you can reliably afford to sac two mountains the card is weak. Usually this just ends the game as the last card the turn before your opponent was expecting however the beefy 4 damage does occasionally make it worthwhile using midgame to wipe out a big dork and keep swinging.
Burst Lightning just pips Chain Lightning to 4th place and this is primarily because of control decks preferring the flexibility and instant speed of the card to the raw power of Chain Lightning. Neither 4 or 3.6 are huge scores which are the respective normal and kicked options however this rating does not reflect the range of the card. One mana spells are premium early game and high damage burn spells are much more efficient late game and Burst gives you a decent offering for both scenarios.
Chain Lightning might as well just do three damage, I have never yet seen the fork ability get used which is quite remarkable. In theory it would be cool on a Swans of Bryn Argoll but further applications for it I struggle to find. In very aggressive decks it is pretty close to Lightning Bolt but in control it is rather more tedious and sees much much less play even with its very solid score of 9 and having the premium one mana cost.
Incinerate is quite a step down in power from the premium burn but like Lightning Bolt is highly consistent. The anti regenerate effect is very marginal but does at least come into play now and again unlike Chain Lightnings ability. Three damage at instant speed is desirable and although it is not very mana efficient it is far easier on your red which is highly relevant in two or more coloured decks.
Searing Spear is obviously just another Incinerate for all intents and purposes. Redundancy is nice but that is not really a thing burn in general lacks, in fact it works against Spear quite often. You want another burn spell but already have Incinerate and find you would rather play something else than Spear which gives you a different kind of effect.
Searing Blaze is rather like Arc Trail in that it can be utterly unfair or somewhat weak. Most decks now run dorks and so Blaze's inherent weakness over other more reliable burn is less and less an issue. When it is weak it is far weaker than Arc Trail at its worst however when Blaze is strong it is the best burns spell in your deck. It scores a massive 18 when it deals 6 damage for two mana and this would theoretically be 36 if you managed to kill off a creature and a planeswalker at once. Because it is so off the charts good when at its best, which is not that hard to engineer, it is well worth playing and risking it being bad.
Seal of Fire is a highly underrated burn spell that does wonders for your mana efficiency and burst output. It is not uncommon in the cube to need to kill something with 5 or more toughness on turn two or three and it is often the case that you have sufficient burn just insufficient mana. Burn heavy hands in general are irksome as you often have to waste the early opportunities to use your mana if you have no targets to kill. Seal of Fire is always happy to be thrown onto the table for later use. It may seem marginal spending just one mana a few turns earlier than you need to spend it but it is just much easier to overlook those kinds of benefits and is far from marginal. Typically this is more of an agro card than a control card but is playable in any deck. A score of 4 is low, probably the cut off point for playable, but if it fulfils the criteria of costing you zero relevant mana then it gets a very healthy score of 8.
Lava Dart is my final burn spell of choice, it is low impact but highly flexible. It can be more game changing that Arc Trail in the right circumstance and also offers high curving efficiency like Seal of Fire. It is also a card you still get most of the value from when you discard it for whatever reason. Another perk it has over cards like Arc Trail is that is is very hard to play around having it kill two of your dorks, against the Arc Trail you can simply stagger your low toughness dorks so that you never have two in play however Dart happily waits around to get its second kill.