Flamethrower has the same issue it had when it was released as a capstone skill in Stormblood, it's not interesting nor effective enough by itself to warrant being the level 70 skill. You really shouldn't have to even think about whether a capstone ability is beneficial to use or not, it should be obvious enough to distinguish itself. You don't see summoners having to do math to figure out that, yes, summoning bahamut is a 3.7% dps increase. It needs to do more than just be a slightly and conditionally better spread shot.

1. Why doesn't it interact with the heat gauge at all? It's kind of a flavour fail to have a move called flamethrower that doesn't affect your heat. Maybe it maxes out your heat gauge so there's a bit of depth to having to spend your heat before you go into flamethrower. Or if having even more heat gain/hypercharge spam is boring, make it drain heat while channeling but make the exchange rate so good it's a no brainer to use in aoe, maybe even single target (e.g drains 10 heat/deals 200+ potency per tick for up to 10s total).

2. Being a 10s channel it has poor synergy with the short 20s cooldown of drill/bioblaster too. It's annoying enough finding safe windows of time to complete a full hypercharge without drill coming off cooldown halfway through. If it were up to me, it'll be a 1.5s cast or something that just winds up and deals all 1000 potency instantly. You could tweak the numbers for sanity, but it's not like machinist doesn't need a bit more damage, and I wouldn't mind having to use it in single target if it were that good. It's kind of strange to have a capstone ability you don't even touch in most boss fights.

As things are flamethrower is tuned way too conservatively both in numbers and gameplay. Bard is already the undisputed king of long term sustained aoe via multidotting different targets, nothing wrong with machinist filling the 'burst aoe' niche in turn.