I just ripped a fair-sized tear in my new cushioned vinyl kitchen
floor, the tear being two sides of a triangle about 10-15cm long.

If it`s a fairly "neat" rip , then you can try gluing it down or using double
sided tape.

If it`s not a neat rip , and you have have a spare offcut, then cut out a neat
square and insert an identical piece from your offcut into the gap ( gluing
etc.)

I did this second method fairly successfully after the dog ( when she was a
puppy) decided to try and tunnel a hole in the newly laid cushion-floor.on the
kitchen side of a closed door.
The pattern consisted of squares so I just cut out a square and inserted an
identical square fromthe offcut .

It was virtually unnoticeable when I had finished.

A useful tip when shifting fridges, washing machines etc. when you have cushion
floor is to slip a bit of carpet offcut UNDERNEATH the machine to be moved and
then it will move/slide easily over the vinyl without damging it.

HTH