Can I select notes in a few channels and move this in FLStudio?
Yes, you can! shift+click on all the channel selectors that you want to copy (they will light up with a green border when selected). You can also double-click on one of the channel select buttons and it will select (highlight) all of them.
To copy the midi in each channel selected press ctr+c
To paste the midi into a different pattern, press ctr+v.