One item has a Recolour option: the Master completionist cape.
Wear the cape, then choose Recolour. That opens the colour picker. It only works while the cape is worn.
| Item | How | Tradeable | |
|---|---|---|---|
 | Master completionist cape | Recolour while worn | No |
A Custom Item Token buys a custom cosmetic that is already dyed. That is not a Recolour kit, and there is no NPC that recolours other items.
See Custom item tokens.