To make a comment on all the "flare gun," "can of hairspray," etc ideas... even to some extent including my idea on making Firebug grenade launcher ammo incendiary, which was before I had thought enough about the problem...
The Firebug's problem is not completely new, but it has been made worse by the release of the new weapons for the other damage-dealers. That's not the root cause, but it made it a lot worse: The perks the FB was already sometimes struggling to compete with got a bunch of powerful primary weapon upgrades.
This is why the Firebug does not need a side-arm or a side-grade. He needs a bigger, better primary weapon.
That means a more powerful, higher damage version of a flamethrower. Or upgrade his current flamethrower to do more damage, have more AOE and burning, etc. Nothing less than this will "fix" the Firebug.
Only after this does he also need more viable options for secondary weapons. The "side-grade" ideas, like incendiary grenade launcher ammo are not a fix, but they can help. In short, like all the other perks already have, he needs options. But mainly, just like all the other perks got with their recent buff, the Firebug needs more damage on his primary weapon.