Whatever you do, stay away from ammonia. Ammonia may seem like a strong agent that will get anything up. However, it won't clean up a mess without leaving destruction behind. Using ammonia will cause discoloration to your vinyl flooring, and it may even cause it to thin out.
Instead of the harsh products you may think will get the job done, go for a softer approach. Take a soft cloth and dab on some WD-40. Gently rub the stained portion of the vinyl flooring until the ink rubs away.
After you are done cleaning up the ink, you now want to wipe away any excess WD-40. Therefore, take another soft cloth that has been rinsed in soapy water and wipe the entire area clean.