How can you place Vinyl floor tiles directly on the sub floor?

Usually. Most peel-and-stick vinyl tiles have a decent glue and will adhere to a clean and relatively smooth subfloor. Make sure it is not OSB or particle board subfloor as peel and stick will not adhere

I would recommend priming the subfloor with an oil-based primer first. If it is plywood, make sure it hasn't delaminated. Vacuum the subfloor thoroughly first. Paint and glue don't like dust.