REMOVE A 1/4″ OF CEMENT!
ARE THEY KIDDING!
For Commercial vinyl tile the cement floor must be sound, clean and reasonable level.
Sounds to me like your 8 year old paint need to be scraped down to the concrete floor, then if all else is well just go over it with a quality vinyl tile adhesive.
The only way I can see grinding a 1/4″ of concrete is if the existing concrete (not paint) is very “lumpy”
And if this is the case vinyl tile is not the product for you!
Maybe ceramic tile or carpet….
Hope this helps