Even though Flash has a skeletal animation system you won't be able to use it in construct, instead you will need to export each frame as a separate image...[ ]
Small correction: Flash CC and CC2014 no longer have any bones - the skeletal animation system was removed due to the shoddy implementation. And only the latest version of Flash has a good graph editor.
You also do not have to use Flash to draw your character parts for later use in Spriter - any app that you can draw in can provide those, including InkScape, Illustrator, Krita, Photoline, etc. As long as those parts can be converted to bitmap cut-outs for import in Spriter.