Will a '71 Demon Grille fit my Flat-Nosed '75 Dodge Dart Sport Coupe?

You can't swap just the grille. Or at least, you won't be able to just bolt the earlier grille in without making brackets, cutting, trimming, and maybe custom headlight surrounds.

Looks like you "flat nosed it" by cutting up the original beak header panel? Grille will be all custom for that. You could use a 70-72 hood, hood latch support, bumper, grille and valance and fenders. Basically convert to an early front clip. The issue with that is you'd have figure out the bumper bracket mounts, because your car has a shock mount front bumper and the mounts for the brackets are different.

But yeah, I don't see a stock grille bolting into what you have anymore.