How do you currently clean it would be the first question and how old is it? The shine may have worn off permanatly. I'd highly recommend buying or borrowing a steam cleaner or steam mop. It will "steam" out the dirt that collects. To bring back some of the shine I would wash again with a water and vinegar mix. Steam and vinegar/water is all I ever use on the vinyl floor in my mud room. Still looks new after 15 years of heavy use.

Years ago we were prepping our house to sell. We had a similar situation. I didn't care about long term cleaning. I just wanted it to look good to sell. I used Mop-n-Glo to bring back the shine. It builds up over time though.