Presuming we're going with a standard Flamethrower at a very close range (find a prop, flame+flare before it can run from it's hiding spot), the very minium amount of damage that flamethower is going to do is about 7 hp. That's just assuming you click your mouse button only once and not holding it down for a second or two, nor is it taking into account afterburn damage. Considering those of us who use this method typically hold down our M1 button for about a second or two before flaring, it's going to end up doing about 20-30 damage, still not taking into account afterburn. By the time the flare hits, between the damage of the flamethrower and the afterburn while switching, that prop is likely to be dead. If not, it will be in another second due to the afterburn of the flare.
Now, as for the degreaser, which I personally use, it does about 1 hp less of damage both with the actual flame and the afterburn (which, with the almost instant switch to the flare, the afterburn gets replaced by the flare's anyways). This typically leaves the flare needing more time for the afterburn to kill a prop or the initial flaming needs to be done for a slightly longer time. Both options I use depending on if I know who I'm flaming or the location of the prop. I prefer leaving the prop to slowly die at the hands of my flare's afterburn, but I can't do that when there are people who can still manage to get health before that afterburn kills them.