<<Disclaimer: Verify this information before applying it to your situation.>>

For those of you looking to find a dairy-free alternative to use in pudding mixes, drink mixes, whatever you put milk in and cook (or any non-cook dessert-type thing): try coconut milk (the regular kind, not the "lite" or "reduced fat") -- it is healthy for you (good fats, even if other people tell you otherwise), and generally, the taste, after baking, is not as strong as you would imagine. 
It's also REALLY yummy mixed with Mori-nu brand chocolate pudding mix (one package to one can, in the blender, then 'fridgerate it for about an hour). ONLY the chocolate flavor is GF, it uses potato starch. The Vanilla flavor uses oat flour as a thickener (and it's also tastey, but it has oats, so you know what THAT means).

Good luck, happy substituting!
JenG

*Please provide references to back up claims of a product being GF or not GF*