do you mean resilient sheet vinyl or real linoleum ?

Painting sheet vinyl is theoretically possible if you scarify the wear layer on top with sandpaper, but it wont last to long and may need to be recoated from time to time.

Real linoleum is made with linseed oil so I very much doubt that application will have much success.

That said, there appears to be a little information floating around the net about it.

have a looksee.

http://obscurity.ws/search.php?query=painting+linoleum

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