Seal up the cat-flap and be strong. I know it is difficult but your cat will eventually get used to it, although the want to get out may never go away it will get better.
When she starts crying and clawing at the door, try to take her into another room and distract her by playing. Try putting something in front of the cat-flap door that covers the flap for awhile. Just stay strong, it sounds like the worse adaptions are going well for her, like scratching post, litterbox etc. So that is a good thing.
Do you all have a backyard?