I have an indoor kitty so I don't know what to suggest for the catflap bit.

However, I would certainly say that my Waffles is a lap cat because she follows me everywhere and likes to sleep on my lap all day but she does go through phases. Sometimes she won't sleep on my lap and prefers her comfortable little beds (which is a relief sometimes because they were expensive lol) but at the moment she is all over me and won't go away
I think it just depends on their mood and you will find that cats really make their own rules which can be ---- >
Something I will say is that you can really bond with your cat by playing with her. If I play with Waffles a lot she seems to want to be with me more but if I am particularly busy then she kind of sulks lol.
When I first got Waffles I used to sit on the floor reading a book and she just came and sat with me out of curiosity. I think the fact that I wasn't staring at her helped because I read somewhere that cats don't like eye contact.
Good luck and hope you are able to put your mind at rest.