How should I request flight following when I'm not taking a direct route to my destination?
I would make the request as:

(controller) "N12345, Say your request"
(you) "N12345 request VFR Flight Following from Madison via the Joliet VOR to Cox Dayton; Altitude 5,500"

I don't think all the intermediate points matter, and I think the controller will quickly figure out what you intend.

They may ask for some clarifications, such as:


"Say your equipment"(they're asking if you have a Mode C transponder)
"Spell waypoints"(they want the phonetic alphabet of your waypoints because they are unsure)