I know that there is a chance that you can find a beehive in a flower forest in Minecraft and that you can spawn one in with a sapling next to a flower, but what are the chances that a beehive will actually spawn next to a tree (Grown by a player), and how exactly do I do it?
A 5% Chance. However, for that chance to start happening, you'd need to make sure that a flower is no more than two blocks away from your oak/birch saplings, and that the flower and sapling are on the same elevation.
As quoted by the MineCraft Gamepedia;
"5% Oak or birch trees grown from saplings that are within 2 blocks of any flower on the same y-level have 5% chance to grow with a bee nest containing 1–3 bees."