Yikes, having had a beauty shop for 20 years, I have had to remove hair dye from a lot of things. However, some dye spills on a no wax vinyl floor cannot be completely removed. I know the faster you get after it the better results you will have. Putting alcohol on a rag and blotting the spot, turning the rag so you have a clean area each time to blot. Here's a site that can give you additional suggestions.. http://www.naturalhandyman.com/iip/author/armstrong/infvinylclean.html
Whatever you do, don't use a cleaner with stron chemicals because it will destroy the "no wax' part of the floor. Also, mixing any bleach products with the ammonia in the dye can create a toxic reaction! Do you have of those green scrubbies? Put some regular white vinegar on a scrubbie and scrub the spot.