Can you paint linseed oil putty with water based paint?
Normally you can use latex over oil based products (never the other way around) if they are fully cured and dried. If the putty you are referring to is glazing compound, then you may have to wait a bit longer for it to cure. Glazing is very slow to cure and take paint. If you can still very easily dent it with your fingertip, wait, the solvents have not yet evaporated.  You certainly can test a small area and see how it goes.  However, don't be surprised if you get some peeling in a few months. Oil based paints are hard to find now, but would work better. I don't know what product you used, but there may be some recommendations on the can about painting.