Tie the flap open until they get used to going in and out through the
opening (or remove the flapping door).

Hugs,

CatNipped

Misty hated using her head too and Sonny will ask us to hold it open
for him if he sees us nearby because it pinches the end of his tail
when he goes through, so he runs through it as fast as he can.

If there is a magnet, try taping it or removing it for now to make the
flap less resistant. To train Sonny,  I was on one side with his most
favourite food ever, tuna, and my husband was on the other.  He would
gently push Sonny's head and body until he was in far enough to see the
tuna, and when he got his nose close to the tuna, I pulled it away
until he went through the flap, then gave him his reward. We did this
for about 3 days, then he did it without being pushed through, just
with the smelly tuna on the other side which he couldn't resist.
Eventually, we were able to take the tuna away.

Their brains see the flap as a wall. Some cats need a lot of practice
until they realize they can go through this "wall".  

Sonny's mom.