How to install vinyl tubing for bathroom vent?
Make a 4" dia plug from a 1x6 or plywood, screw eyelet into center, clamp plug into dryer vent with worm gear clamp.  Pull through with your fish tape.  Perhaps a taped cone could be centered over the plug (and the fish tape lead through the center, for better insulation tracking).

Down the road this lint brush will remove any buildup.  This one has a 10ft shaft.



I'd urge you to convert to smooth walled metal duct and add a screened vent wall cover or a spring loaded damper.