You need to put the file "flyout_revisited.css" somewhere that it is accessible (probably assets/templates/wayfinder) and then modify your TEMPLATE file to include that CSS file.
The snippet call that you showed wraps everything in a "leftMenu" id and a "leftBlock" class, and so the existing CSS may style those in a way that is incompatible with the "flyout" styling.
I would start with a very basic non-styled Wayfinder menu (even just in the content part of some test page)
[[Wayfinder? &startId=`0`&removeNewLines=`1`]]
then get the "flyout" stuff working and only THEN incorporate it into the left-menu block.
Do one step at a time, and if something breaks, then undo it!
Good luck
Gordon