Didn't even know fletch was a word! ... apparently with three meanings:

1. noun (archery). The vane toward the back of an arrow, used to stabilise the arrow during flight.
2. noun (fisheries). A large boneless fillet of halibut, swordfish, or tuna.
3. verb. To feather, as an arrow.

So, I'd say any emoji containing an arrow, a feather, or even a fish, might work. Couldn't find any halibut, swordfish, tuna or fillet of fish emojis, which leaves:

• U+1F3F9 BOW AND ARROW : 🏹
• U+1FAB6 FEATHER       : 🪶
• U+1F41F FISH          : 🐟

I'll leave the final decision up to you. :)

👁️🍾👍🦟