Borax substitute for swirl painting
There are lots of alternatives to Borax online for making "slime," but I don't think the rubbery texture will work for you. The closest non-Borax idea I found that might meet your needs is to use either colored Jello or plain powdered gelatin (it's often in the vitamin supplement section of a drug store or pharmacy, or in a grocery store in the baking products aisle), add the amount of boiling water that after mixing well will flow enough for painting, but will dry down enough not to be sticky. 

You should probably experiment with different amounts of water and /or gelatin, as well as different cooling times, before applying, but this is a really simple, inexpensive, legal "recipe" and has the added benefit of being edible.