What kind of windows do you have?

I installed a cat flap in a double-hung window by closing the window onto the top of the cat flap, screwing the cat flap into the bottom of the window frame and then adding a piece of Plexiglas to the remaining open window area. I attached the Plexiglas with small screws and caulked all around everything. That would work with a sliding window too. Just put the Plexiglas above the cat flap.

It's been in for about 3 years and still holding up well. (Of course, I had to take out the screen.)