Possibly, but more leaning towards what others say aka no.
Jewels are like Convicts when they breed. They get very aggressive. Firemouths, like most (perhaps all) other Thorichthys species can be very aggressive and put on great threat displays, but have no brawn to back it. Well they do, but not enough. If the jewels wish it, they'd prolly kill the Firemouth.
In rare cases it could work, but chances are the Firemouth will have a tiny bit of territory and lead a rather miserable life.
So if you get two non-breeding jewels (they're also like Convicts when they're not breeding, kinda aggressive but not overly so) and a Firemouth, they can all mix and mingle. But I would definitely suggest against a Firemouth and a breeding pair of Jewels.