We want to lay flagstone over our cement patio. Can we do that without using motar? We would use sand to level where necessary and plan to use decomposed granite as grout.

if you do, you'll be 1st as sand has no strength to prevent flagstone movement,,, for centuries man has laid stone w/o mortar but not in your application.

If we grouted between the flagstone wouldn't that help hold it in place?

can't hurt but, still, its laid on mortar, NOT sand