At this time we do not have a separate KDF fleet on PS4, I would need add a leadership position and person to handle day to day KDF related projects/operations -we barely have 50 characters in the main fleet at this time but it is certainly an option in the near future. In the meanwhile, let me see if I can add your KDF character to the main fleet (things work a little different on PS4, it's worth a shot.) What is your KDF Character Name?
I tried sending you an invite (it gave me the message regarding your characters' incompatible allegiance), it looks like Cryptic has the same FED / KDF arrangement as STO PC. In the near future I'll send out an announcement to see if there is enough interest and people to create a KDF fleet :)