I'm installing CoreTec One vinyl plank flooring and I've had trouble finding directions on how to rip it to width. Most of the "vinyl plank" installation guides I've found are for thinner, more flexible product which can be scored and snapped. I've seen suggestions that one can use a circular saw but I can imagine the vinyl might gum up my table saw. If not, that seems dead simple.
It cuts just like wood or MDF. I just installed a vinyl plank floor and I was able to do cross cuts by snapping and scoring, cut around door jams using a jigsaw and rip it to length on the table saw. Some brands snap more easily than others, I have had to use a miter saw for a whole floor instead of the score and snap method. If a crosscut was too near the end of the plank I did have to use a miter saw. It produces little vinyl chips kind a like sawdust but a little bigger and they can be vacuumed up easily.
In your position, I'd try a fine toothed blade in a table saw for cutting the vinyl planks. As long as the material keeps moving past the blade, I wouldn't expect a problematic amount of melting/gumming.