Painted my basement floor and now it is rubbing off in the kitchen carpet. Any suggestions
How do I stop it?

You can't. Cover it with laminate, tile, or carpet, over a thick vapor barrier well taped at all the seams.
Basement floors are often too damp for paint, or for just about anything. The concrete effloresces. a powdery mineral deposit from moisture, and it pushes paint right off.

Agreed, instead of paint you could have used concrete stain but too late for that now