First off, go easy on it. You don't want to damage the smooth inner
layer of the flexi.

(solid fuel flexis have a corrugated outer layer, and a smooth inner,
with the edges of the helical inner winding facing downwards - the
idea being to reduce places for moisture/tar to get trapped and start
attacking the stainless)

I use conventional rods & brush - but the angles aren't too tight it
mine. You might like to look at hiring the kit, using a professional
sweep, dragging a brush through on a rope from the top - or simply
caving in to the cost of good rods.