Modern Burn!

With 8 spells that deny life gain and do dmg, I think its covered, Stigma Lasher is slower and might have trouble pushing through.

Actually it IS modern legal :P Monastery Swiftspear is amazing replacement of Goblin guide or even as guides 5-8, Im afraid BloodFire Expert is too slow and dies to anything in the format without actually doing anything.

The list usually runs 4 Goblin Guide in place of the Monastery Swiftspear, but the monk makes it a lot more affordable for some people trying to get into the format, with minimal to no losses on the dmg output (and without fixing their hand).

I think that Shandra's Spitfire is a better option then Kiln, only because she's flying. You are getting rid of haste which might or might not be extremely important to the build. Flying is a good substitute if no other options are available. Not to mention that +3.

Edit: Chandra's Pheonix might be a good substitute too! She has flying, haste and can come back from the dead, however she lacks the ability to grant you that +3

Spitfire has a higher CMC, though. and it's ability is dependent on dealing damage, not just the casting i.e, Kiln Fiend is better against decks that negate damage.

Chandra's Spitfire and Chandra's Phoenix are too slow, specially in a format where Path to exile is the most widely used removal (with bolt). Kiln fiend could be a replacement of Hellspark elemental, but again.. too slow... Burn it's all about getting them to 0 as fast as you can, and the Kiln totally sets you back turn 2 with no dmg.

alright, fine. I'll give you Spitfire, but Kiln fiend too slow??? Really?

He has the potential to swing for anywhere from 4 to 7 to even 10 damage on turn THREE. (+whatever you're getting from burn spells) If that's too slow for you then Idk what to tell yah.
Yeah, maybe he doesn't have haste. But if you want large amounts of damage in the early game, then he's your guy. I just don't see how he's too slow for this deck/format. Personally, I'd run him over Swiftspear 9 times out of 10 without batting an eye.

Yeah I don't mean he's bad, he's pretty awesome, but in a lot of games I have played with the deck, dropping a creature turn 2 and letting your opponent untap without doing any damage at all I consider it slow, he will die to a bolt or to anything else in the format, we will be chump blocked next turn or whatever, thing about creatures like Hellspark Elemental (or haste in general) is that you can push up to 6 damage with one card in the right moments (when he taps to put board pressure cause you are all spells), most haste creatures do this. The Kiln actually just get worse in multiples, and at least Hellspark Elemental is not dead to Liliana's discard and similar.

Those little bits of extra consistency in burning your opponents life total specially during turns 2-3 are whan make burn competitive, if you trade a turn with a non hasty creature that will be removed or blocked a turn later (even while dealing burn dmg) it slows you down and your winning chances slim down. One thing to note is that depending on your hand, Kiln puts you in an awkward position while doing some "bad" choices, you usually want to put your creatures first on an empty board, then use the least flexible burn and leave your best for last, but Kiln forces you to burn when he attacks and with multiple Kilns in hand, become an awkward problem, as you might spend to much setting up without dealing any real dmg.

At last, Monastery Swiftspear can be saved from a blocking Snapcaster or a Bolt by burning your opponent, making him trade his options, Kiln can't do that, and Hellspark Elemental at least pushes 2 dmg through a blocking Snapcaster while being able to come back for 3 more. I'm not saying Kiln is bad, he's just IMHO not the best option.