Story-wise, I guess in a video game, they'd kind of be filling in for the "core" Sonic Team while they're off on their own adventures? Frontiers seemed to want to spin Sonic's "main" cast off into their own games...which was probably just setting up for the DLC, but still. Or they could just be...Sonic's OTHER "family"? Maybe they could be on the other side of the world from where everyone else is, and only Sonic can realistically get all the way over there to visit and help them out?
Still, I think they could work more as "sneaky spy specialists" than Sonic's main game team. Kind of a Sly Cooper band of underground fighters, rather than the rather public frontal assault characters. The Freedom Fighters could be more "Splinter Cell" than Tails and Amy's "Wolfenstein"? I'll admit, they might fit a little better in their own game, rather than a pure-Sonic game.
Gameplay-wise, I think Ian Flynn already gave us some ideas in the post-Genesis Wave Archie comics. It would kind of depend if they'd show up in a 2D or 3D game, I guess. In a 2D game, I think you can just get away with everyone just being a re-skin of Sonic. They'd just be in there for fan-service, but I think there WOULD be people who would pay for Freedom Fighters DLC, especially if they get their own story in the game. Just give them ONE unique move and I think you're good. Like a rocket punch for Bunnie, or the ability to see the whole map to find secrets easier for Sally.
Making them work in a 3D game might be a little trickier while still getting their personalities across. Though, you COULD just stick them into the same mold as the Chaotix. Since Vector, Charmy, and Espio COULD play fairly similar to Bunnie, Antoine, and Sally. And I'd probably make Rotor more like Omega/Gamma, myself. It'd be nice for the Freedom Fighters to have their own things, though.
For Sally, I'd probably play up her using Nicole. Nicole would probably be back to being a palm-pilot like in SATAM, since Sega probably wants to avoid getting too close to Archie canon. Either using Nicole to create hologram-like weapons, or using technology to distract and sneak around enemies. Maybe give her some ninja-like moves, for sneaking around and quick attacks. Maybe some sort of cloaking ability.
For Antoine, I'm thinking gameplay like Link from Legend of Zelda. A lot of dodge-rolls and slashes. A little quicker than the other characters. Maybe some flips. Maybe some sort of Assassin's Creed type "sneak attack" from behind, since he's still a little cowardly?
For Rotor, maybe a mechanic where he can build weapons from the parts of enemies he defeats? Kind of Ratchet and Clank sort of thing where he has a bunch of crazy weapons? He'd also be the heaviest and slowest, so I guess we'd have two tanky characters with him and Bunnie, and two more fragile but faster characters with Sally and Antoine.
For Bunnie, yeah, she'd be a tank. Maybe a little bit of Bionic Commando in there with her grapple-arm. Maybe a little bit of original God of War, turning her arm into a attack-chain-whip. I'd probably make her the strongest core attacker of the group. Rotor would have more powerful weapons, but you'd have to build up to those. Bunnie would be strong right out of the gate. And I think it makes sense for Bunnie to be a little faster than Rotor.
Maybe these don't quite work, but I think there are ways to get the Freedom Fighters to work in a Sonic game. Plus...I just want it to happen!