No, Triangulated Fire ignore all other MODs, not even "ignore all other MODs unless specified" so there is no need to look into if other MODs specify they are compatible or not. Nothing stack with Triangulated (in terms of BS MOD).
Triangulated Fire denies the application of any other MODs to your BS stat besides the stated -3 that it specifies.
if you meant the 3-member Burst bonus, yes it apply. MODs means Attribute MODs, Burst will still apply. nevermind, you don't have burst bonus to Entire Skills anyway.
There's BS/WIP/PH MODs and there's Burst MODs. It is generally considered that Triangulated Fire only cancels BS/WIP/PH MODs not Burst MODs. This is not actually supported by RAW, but is the way it's generally played. In any event (as pointed out above) you can't apply the Fireteam Burst MOD to Triangulated Fire because it doesn't apply to Entire Order skills. This is separate to whether Triangulated Fire does or does not affect Burst MODs.