I have done this before and the trick I used was to glue an old piece
of carpet to a piece of 1/4" plywood. The carpet will slide along on
the flooring not to be harmed while the 1/4" plywood will be used as
the surface to which a pry bar can rest upon.
The hardest part is getting it started. Once started, slide the
carpet-plywood jig along under the edge of the old sub-flooring, using
the pry bar to pry little areas at a time. In my case I was able to
free a couple feet section and then grab a hold to it with my hands and
lift up. Usually several feet came free at a time.
Take a circular saw and set the depth to cut through the two layers of
vinyl and most of the way through the plywood. Then cut a checkerboard
pattern on the floor before you start prying. The smaller pieces will
be easier to pull up and dispose of. Dust mask and goggles are highly
recommended esp. if the vinyl turns out to be asbestos.