In 2016, Swapdoodle began to allow for the use of badges from Nintendo Badge Arcade, but Pokémon badges were not available from the get-go. However, all Pokémon badges obtained in Nintendo Badge Arcade can now be used within Swapdoodle. This allows you to hand-write and send messages to your friends, now with the ability of attaching up to four of the badges you have collected in Nintendo Badge Arcade into the message.
Source: Serebii
Pokémon Blog 