They might, or perhaps something like the thin plastic (flexible) cutting board sheets. We need to know more about how your slide is supported, e.g. does it ride on skids, rollers, or does it float above the floor most of the way in until it gently tips down and rest on its feet. Also, how does the height of the vinyl compare to the previous floor covering? Is it higher or lower?
Is the problem that the slide stops moving and won't go fully in/out, or that it is damaging the vinyl by scraping over it?
Some slide mechanisms are adjustable; others not so much. What brand of slide hardware do you have?