I agree, a flower pot won't work. I have seen it contained successfully in a garden, in the ground, and how the owner did it was to use a galvanized metal dustbin or trashcan, originally intended to contain ashes from fires, about 3 feet feep and 18 inches across. He cut a foot off the bottom, dug a huge hole and inserted the the whole thing, leaving a rim of about 2 inches above ground level, then filled it up with soil and planted the mint. If you're prepared to do the digging necessary, I don't see why that can't work with a plastic trash can of similar dimensions with the bottom removed, but whatever you decide to use, it needs to be a minimum of 18 inches deep into the soil, and intact all the way round. Laying bricks under ground with mortar between to form a solid, wall like barrier doesn't last long; as the mortar degrades, the mint escapes.
If you want a smaller patch of mint, something like an old chimney pot or stove pipe that's deep enough should do the trick, but you might find, if the patch is only a few inches across, the mint starts to fail after a year or so from being contained in such a small area.
It's possible that some root rhizome barrier material, more usually used to restrain bamboo, will work so long as it goes down deep enough,but keeping it in place while you backfill with soil is a bit more difficult than inserting a rigid object. Either way, it means digging a deep hole...