I received this item from the Flowering Cactoid hunt, but I was unaware of it's future value at the time and sold it. Now I need the item again for the Barheim Key side quest. Is the ANY way to regain this item?

As far as I know, there are not items that would destroy your chances of gaining the Barheim Key if you were to sell them.

The item you're talking about should not be a loot item. You may have to speak with Dantro a second time for him to give you the flower, he does not give it to you as a reward from the hunt.

I got it as a drop from the mark. Then I sold it to a merchant. Now I need it back to get the Barheim key. I'm not sure if I can just look for the hunt creature again and try to kill it, or if I can buy it back, or whatever.

Are you sure it isn't the Cactus Fruit that you picked up from the mob?

I would suggest talking to Dantro again, as I said there shouldn't be anything required to obtain the Key that can be sold.

You can never miss your chance of getting the key, there's just an extra item you won't get, which can be bought for a relatively low amount of Gil anyway.