soundstart=Flamhvy1;
soundtrigger=0;
Soundtrigger=0 means that it will not just play one sound clip, but instead plays the sound every time it fires. It's a problem with BA, basically. BA is full of junk and bad practices like this. I do not recommend it as a reference, nobody maintaining that mod has done a good job of cleaning it up or fixing stuff like this, frankly.
See how I set up the machineguns for the Heavy Shells in P.U.R.E. (Heavy_Shell_Gun)- it's a single sound, using Soundtrigger=1, that sounds like 5 shots being fired, which fits the burst timing perfectly. With flamethrowers, it's straightforward- just make a sound that is as long as the longest possible burst (usually, this is a second or two, with timing that allows for continuous fire). The "worst" thing that happens is that the sound is trailing off but the burst has already been ended by Spring's code handling bursts (it treats them as single shots, basically). As an alternative, it's quite simple to make a weapon fire a pre-determined number of shots via COB (or, for that matter, a random number, and new stuff in SVN lets us play with other nifty things as well), so you could have a flamethrower that was forced to use a burst-length that matched a sound-length (and some BOS code to lock it from rotating the originating piece while doing so is trivial).
In short:
A. Soundtrigger=1 works just fine, and plays the sound ONCE per BURST. Not the other way around.
B. To get the behaviors you want, you can take a variety of approaches, even going so far as different sounds with different lengths to reflect different lengths of bursts forced via COB. It's not really hard to do unless you're totally stuck with COB stuff, in which case, you need to sit down and learn how it works, or settle for sounds that may keep playing after the weapon has really quit firing, which with a flamethrower isn't a big deal anyhow, frankly.