I have sewn on vinyl, both the clear stuff and other. With the clear I made my big dog a raincoat, with a hood. He hated being inside so he needed some protection. I did not use a special foot because I did not know there was such a thing. Never thought about it. I did use paper though, just typing paper between the foot and the fabric. And lots of tape, since pins don't really work for a raincoat. I just used masking tape where you would normally use pins.
I also had to make a bunch of black vinyl Christmas stockings for a gal. Those weren't too bad because the vinyl had a backing. But I sure went through a lot of needles.