Milly didn't pick up the whole cat flap concept very easily, even after watching Geoffrey do it. We did literally have to post her through it each way - and every time she wouldn't come back through but bolted in when we opened the door, we would pick her up, take her back outside and post her through it again.
Eventually she worked out going out but not coming back in
I watched her for a while and realised she was pushing on the door not the flap to get back in. Having read a bit about cat eyesight and colour contrast we concluded that she could see the light outdoors when looking out, so knew where to push, but the contrast was much less when she was looking back in, so she couldn't tell which bit was the flap. We solved this by putting some yellow/green striped earth insulation tape round the outside of the flap to provide a better contrast. She soon worked it out and then a couple of weeks later I started removing the tape a piece at a time, and she still uses it fine now.
It's also just worth checking that it's not too high and they can physically reach to do it. When Sooty (RIP) got old he stopped using the flap and we posted him half way through and watched him, and it turned out that with him getting slightly arthritic, it was just too high and he couldn't get his back legs through...one 'step' made of paving slabs later and he could use it again.
