I just couldn't digest the flapping airplanes.

They digest quite well with a grain of salt.

They were modeled after the early jet prototype "Flying Wings". I thought they were quite cool...

Maybe you didn't get the idea behind the (visual) style of the movie?

Actually it is a very real type of aircraft. But remember those on the movie were robots, they did not carry people. See real, flapping airplanes as you call them here:

https://www.youtube.com/watch?v=2Nd8BA3OHCc
https://www.youtube.com/watch?v=poX2Hg9qae0
https://www.youtube.com/watch?v=0E77j1imdhQ
https://www.youtube.com/watch?v=w6VLzKACnS8&t=133s
https://www.youtube.com/watch?v=uUcmJcTL0-0
https://www.youtube.com/watch?v=fBADJ7-elHQ

And we could go on and on and on ad nauseam.