You are right. It will be a problem whenever you drag furniture around.

It can be done with the right size and thickness of stone along with a expertly tight seamed flagstone but for that type of skilled craftsmanship and material you must be prepared to pay a premium for the materials and labor. It is definitely not a first time do it yourselfer project.
You'll have much better success in pouring a slab and mortaring your flagstone if your skill level is below a master mason ability.
below is a dry lay flagstone patio ( shown without the furniture)with dg backfilling the joints. Its been in for over 15 years and has held up very well , the mason that installed it, Randy Shadrick of Outdoor Environments has about 27 years as a mason.

Heavy wrought iron is heavy. I move mine about once every two years. You don't slide it around as you sit down to eat. So it doesn't really matter how it interacts with the paving. You set it, carefully, then leave it there.

Since my 'flagstone' is very rough, raw stone, the furniture is sitting on flat pavers. Otherwise, I'd spend a few weeks evening things out. So part of this is going to depend on how finely cut your stone is. Around here, you can easily buy bluestone that is flat and square. There is no reason it wouldn't work fine for a dry-laid patio. The downside for me is that costs money.