Well, I've had flagstone but not set in concrete. It looks great with a ground cover, like creeping thyme, growing between the stones. Then it won't matter if the move a bit. I've also used fieldstone for paths and dig deep holes to bury them in, with a flat side up. They don't budge.

If you want it in concrete, I guess this doesn't help much. I don't see how it can stay put with the ground freezing and thawing. It might depend on how deep the base is underneath. It will need a couple of feet of a sandy base.

I've got a large flagstone patio that's about 8 years old and it does stay put. The base is a layer cake of 8" of fine gravel topped with about 2" of sand. It was a big job but I was concerned more about drainage than shifting. I live in a very rainy Portland, OR and the mud is horrible. I needed a place for me and the dogs to go on a rainy day that wasn't muddy. It works. Occasionally the smaller, thinner stones shift a bit. Moral--use bigger, heavier thicker stones. I'm very happy with mine.

The base is the secret. There must be adequate drainage below the stone, so that water is not trapped and when frozen expanded thus popping the flagstone up. I did not have any trouble with mine at my former house.