Freefin works with any operative that deals skill damage.
Freefin works best with operatives who can maintain at least one wavehunt stack, however almost all skill-damage operatives can.
Freefin works better with operatives who deal thermal skill damage, but the difference is small, although it gets larger at M2.
Since Freefin ideally only deals damage when she first uses her support skill, and ideally only does that once per fight, that means she also works perfectly with Celestial Swan, even for operatives that don't deal thermal damage.
The best operatives to use Freefin with are
Siris - Ksana deals exclusively Thermal Skill Damage and can maintain max Wavehunt stacks, making her an ideal partner for Freefin.
Fenny - Pureheart deals almost entirely thermal skill damage, and hence works extremely well with Freefin.
Fritia - Hush spends most of her time in combat shooting stuff, but most of her damage is in her ult, which works well with Freefin as Hush' ult is entirely skill damage.
Nita - Pulse deals exclusively Thermal Skill Damage, and can use skills extremely frequently, making her a good pairing with Freefin, however since Pulse' damage scales with Max HP, Freefin's ATK buffs are wasted on Pulse. Freefin is still a very good support for Pulse, but their synergy isn't ideal.
Note that Siris' Ultimate isn't worth using with any current dps operative, as there is no scenario where you would want to swap out your main DPS to have Freefin swap in and start doing damage - you're always better off just maintaining Freefin's support skill and having it buff your main DPS.
Further note that Freefin's ultimate cost 60 U-Energy, which is more than Fenny - Purehearts ult uses and that Pureheart tends to generate via her standard LMB combo chain, which means that the only time you'd actually want to use Freefin's ult is when using Pureheart and are only using Purehearts RMB attack.
If having Freefin support Pureheart whilst Pureheart uses her LMB combo, you'd need to not use Pureheart's ult for a while to gather enough U-Energy to swap Freefin in via ult, which is a large loss of dps for Pureheart.
Siimilarly, Pureheart offers absolutely no support buffs to Freefin at all, so whilst Freefin is on the field Pureheart is basically just dead weight on your team.
If you are using Pureheart as your dps and using Purehearts LMB chain, then it's never worth it to ever swap Freefin in via her ult.
Since Pureheart's RMB attack doesn't allow Pureheart to use her ult, any U-Energy she gains is useless for herself, and thus allowing Freefin to use it for her ult does work, however since Freefin isn't really any better at AoE than Purehearts RMB attack is, you really wouldn't need or want to ever do this anyway, but you could.
As such, I recommend that if you are using Freefin as a support for another dps, then you should never use Freefin's ultimate ability.