It is not possible to recover or reactivate a deleted Pokémon Trainer Club account. Once a Pokémon Trainer Club account has been deleted, it is no longer possible to access any previous account details, including those for Play! Pokémon, Pokémon GO, or any other connected application or service.
Please see below for additional details regarding linked accounts.
Pokémon GO
If you deleted your Pokémon Trainer Club account and used a secondary authentication method (such as Facebook or Google login) to log in to Pokémon GO, it may be possible to recover your game data by contacting Niantic support here (these links takes you to a site not created or maintained by The Pokémon Company International).
Nintendo Account
If you unlinked your Nintendo Account prior to deleting your Pokémon Trainer Club account, you may link that Nintendo Account to a new Pokémon Trainer Club account.
If you did not unlink your Nintendo Account prior to deleting your Pokémon Trainer Club account, you may not link that Nintendo Account to a new Pokémon Trainer Club account.
Twitch Account
It is not possible to unlink a Twitch account from a Pokémon Trainer Club account, including if the Pokémon Trainer Club account is deleted. If a Pokémon Trainer Club account is deleted, it will not be possible to link the Twitch account to a new Pokémon Trainer Club account.