You're very close. So the following hint is something you already know, but I suspect that seeing that what you already know is the problem will tell you the solution.
If you send any cats, one will inevitably land on the zero-flag, and it's game over, you can't walk out. So you don't want to send any cats through. But you still need to have three cats at the start of the room.
As a bit more help, I found it easiest to send the flag first - it can be done a different way, but I found the movement too tight to be worth it since you'll only have one flag to recharge for a long run if you don't send the flag first. Similar to the previous level, the moves are going to be really tight here for a bit regardless, so I'd take the easy route ;)