How Can I Fit Vinyl Flooring Neatly Around My Toilet?

I would suggest you buy a new wax ring for your toilet, turn the water off to it, then flush the toilet to get most of the water out of the tank and bowl. Then unscrew the water line, take the two bolts on either side of the toilet off.
Lift the toilet out, Lay your vinyl down and cut around where the drain pipe is. Then reinstall the toilet.
I know it sounds like a bit of work, but it is well worth it. The floor will look much nicer and the job will look more professional with no cut lines showing.
It is quite difficult to precisely cut vinyl around the toilet.
Hope this helps.