Duplicates are not needed for blooming or second affection. You only need two birds of the matching type, two petals of the matching nation and an elixir of the matching rarity, plus a hefty pile of gold.

They are, however, a good way to get bond crystals, as you get 1000/12000 for each gold/rainbow that you fuse or sell. Bond crystals are used to buy second affection items and danchou medals, which in turn can be used to buy tickets with 92.5% gold/7.5% rainbow rates.