I would first look under a cabinet or dinette, something similar and see it that stick one tile is original? Jayco uses sheet vinyl (fast install).
Next, I would go shopping and find what you like. Ask for a large sample, and let them know why such a large piece (few inches wide and at least a foot long). Go home, and see how it works with the slideout. You can use some double face tape to hold it to the floor, or hold it in place while someone else moves the slideout.
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