A flower in a pot can't be picked when you hold the same flower as the one in the pot. I can't prove it by video or screenshot. Try to do the same thing in creative mode.
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An easy fix for this would be for flower pots to drop their contents at their location as an item when right clicked, much like picking berries and using shears on pumpkins/beehives.
Relates to MC-232489
You cannot use any items at all while looking at a flower pot, unless you sneak.