So to clarify point-by-point,
First off, the benefits of Snapcaster Mage and Past in Flames is to open the door so that you CAN use spells that don't have flashback. If you tie yourself only to items that already have flashback, that's REALLY limiting your options. You said that you pulled Silent Departure for Cyclonic Rift because it's more effective, so why not do the same for some of the other cards given that you can now flash other things back?
Control WILL be a problem as they're going to be hitting you with counters that exile things - Dissipate and Syncopate are very much a thing. You won't have any chance to get things back from the 'yard. Further, if they're smart, they'll see what you're doing after game one and can just counter Burning Vengeance - this leaves you with ZERO options to win.
Aggro still is a problem, as a quality aggro build will kill you by turn four given your current lack of direct removal or blockers. Yes, Burning Vengeance can target creatures, but it requires you to hit your three drop perfectly and then have more than one flashback spell in the yard already to be able to zap them with. That's an awful lot you need to go right just to take out 2-3 creatures. Also, keep in mind how haste will play into things - can you generate three damage at instant speed to deal with a Dreg Mangler? Further, can you do so consistently?
If you're just looking to rip through cards, Reforge the Soul or Tibalt, the Fiend-Blooded are more consistent and cheaper options to cycle things into the yard. Then you still have a hand AND can do things with flashback.
The lack of burn/removal I'm stating is the more direct variety that doesn't rely on you having Vengeance on the field. Again, to manage that you need to have drawn vengeance, get it on the field, and THEN have a flashback spell ready to go... just to deal two damage. Searing Spear requires two mana... that's it.
With regard to Arcane Melee and Devil's Play, if you reduce the colorless X cost by two, that means you can essentially cast it with an X of two for just one red mana. So to that end, it would pump the X to four if you have a second one in play, but otherwise a second copy of Melee is a dead card. It's the same as if you run Pearl Medallion and cast White Sun's Zenith or any other cost reducer like that. In many regards, you'd be just as well off to try running Goblin Electromancer to see if you can get the same amount of use out of it.
Militant would be an easy target, again, assuming you have all the criteria for a vengeance burn to work... nevermind how many spells it might've exiled on your path to get there. Again raising the question for more directed burn spells.
Silent Departure was simply something to work with flashback if you're intent on everything having it. Cyclonic Rift is most definitely a more versatile card (but note the lack of flashback).
So your answer for Thragtusk is that you end up casting and wasting FOUR Vengeance shots? Lest we not forget he produces the beast token when he dies. So that's now shifted you to trading four-for-one. In a world where competitive card advantage is kind of important, that's a trade you would NEVER want to make. Nevermind that Restoration Angel is also a very real possibility, one that definitely doesn't get touched by Temblor. Don't forget creatures with regeneration or that grow beyond immediate burn range like Champion of the Parish - which can easily be a 3/3 or 4/4 on turn 2. Temblor is a good card, but keep in mind its limitations. In my experience, it's a SB card.
For Naturalize - again, great card, but hardly worth splashing an entirely new color for just that. If you were sitting on a full playset of the shocks to get green into the mix, that'd be one thing, but three guildgates just won't get you there. Why not just splash some blue countermagic to deal with those possibilities? Smelt deals with Grafdigger's Cage but beyond that, I think you might have to just acknowledge that Rest in Peace will totally hose your plan.
Again, playtesting will be the best measure, but I just don't see where a deck without any direct, immediate defenses will survive long. It might be a blast to play casually, but in a competitive standard environment, you're going to be frustrated.