His teleport is the only thing I have to look forward to as Johnny Cage. He's absolutely horrible to fight against. Imo, just make his spin more punishable. Make it have a wayyy longer recovery time, because as is there's pretty much no drawback to using it. You can block immediately after!It makes me sad. :___(
I have a tough time as well to beat Kung while playing as Cage. You can punish his hat throws and hat spin with his dash kick (forgot the exact name atm), it will go through projectiles as long as the other player is close enough for it to connect, otherwise it hits you. If they are too far away for the standard one you can use the EX one, it goes full screen.
I usually switch to Kano or Liu Kang to punish them with projectiles if they pick Kung again.