How do I fix sticky KILZ primer?
The problem you are having is not uncommon. It is a basement floor so I'm guessing below grade. There should have been a layer of 10mm poly under the floor when it was poured but either way concrete leaches moisture. This is a contributor to your problem. 

If you didn't thoroughly wash the floor (I mean powerwash) with a bleach based cleaner you will have a hard time getting any product to last. If you can't pressure wash, scrub as best as you can and use an etching acid or solution. Kilz will dry, unless there's moisture or dirt underneath. Will have a harder time overcoming moisture as it doesn't have near the penetrating properties as a specific product like drylok does. But for a floor, I prefer the lasting quality of a concrete epoxy. 

I know it's not your most favorable thought (starting over) so ultimately it's up to you. The right prep and technique with a product specific to the job may save you the hassle of ever doing it again. Best of luck!