I bought a 15" wide x 22" high x 6" deep flush wall safe and was wanting to hide it with a picture on a hinge. I thought someone would make the hinged picture mount but haven't found anything online after extensive searching. I guess I can rig up something but its a little tricky since the hinge pins need to be hidden and that doesn't allow the picture to swing very far. Any ideas?

Just forget about trying to adapt a hinge to the picture frame and hang the picture in front of the safe like normal. Then, just take it off of its hook when you want to get in the safe. Having a picture flat against the wall looks abnormal and is a clue that something is different about the arrangement and is worth investigating.

Try hobby lobby they have framed several prints for me, they could frame something with a heavy frame that wouldn't look out of place and probably have any necessary hardware fore you to mount the picture for the swing you want.