Can I mix tie dye into wall paint?
Not a hard no but you may want to reconsider for a few reasons:


As @dandavis pointed out - the compounds may not work well together.  This could cause long term negative effects.  OTOH it might not.
The hand mixing of paint will take a lot of mixing to get it even.  However, if you're going for a tie-die look this might work in your favor (but probably not)
All paint is sold as white - the paint store will happily, for free (usually) make it whatever color you like at no charge and mix it for you.