"If there isn't any flashing between the hardiplank and the brick chimney (just caulk) wouldn't it just leak at some point?"

Yes, and every time it's painted (at the least) it will need to be resealed. A chimney can, does, and will move different than the house, sometimes a little sometimes more. There is nothing wrong with using the RIGHT caulk when APPLIED PROPERLY.

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Rick Cantrell
Columbus GA