> Would it do the job if I just 2D cut a plain extruded tube surface and flowed
> the knurl pattern onto the remaining pieces?

No, that wouldn't really make any difference - Flow works on a full "underlying surface" - if you cut out a hole in the middle of something it does not make any difference as far as how Flow will be used on it.

Does the model that I attached above that will trim work ok for you?

- Michael