Short answer, deathflare could in theory share the button with enkindle bahamut, but there's one thing that might be keeping them from merging the two. They don't share the same cooldown timer.
I'd have to look at the way the rotation works more closely to see if changing the timers would matter at all (probably it wouldn't) but deathflare has a 15 sec recast time while enkindle bahamut is 10 sec. If they shared a button, and you went straight into summoning bahamut after using deathflare, you'd start that mode with enkindle bahamut already on cooldown, which would nerf the summoner's DPS even if recast times were changed since they couldn't start the phase with an ahk mohrn.
This is the same reason you can't have dreadwurm trance on the same button as summon bahamut or firebird trance. The skill has a 55 second cooldown meaning that if they were on the same button, you'd have to wait 55 seconds after entering dreadwurm trance before you'd be able to summon bahamut.
The job definitely has a lot of button bloat, and there are a lot of ways it would be nice if they could consolidate buttons that can't be used when under other parts of your rotation... but there are reasons that at the current time they do need to be separate.