How do I use my recovery key on a new phone?

If you still have your old phone, Set Up Another Device is easier: see "How do I move to a new phone or switch between iPhone and Android?". Otherwise, install WitnessWork on the new phone, go to Settings → Account → Use a Recovery Key, and enter your key. It works between iPhone and Android. Case, spaces, and dashes don't matter, and the app tells you when a character is mistyped. If that phone already used Buddies with a different account, the app asks you first, and its Buddies data is deleted from the phone. While other devices are still signed in to that account, its buddies stay on them; on the account's last device, its buddies are removed for good. On iPhone and iPad, the key also replaces the account on your other Apple devices that use the same iCloud Keychain. The recovery key brings your account and Buddies identity. If your account has a backup (Settings → Account → Backup), the app then offers to restore your service records, contacts, and notes; otherwise Cloud Sync brings them over once it's on for the new phone (Settings → Device Sync), or you can move them with iCloud Sync, Google Drive Sync, or Settings → Backup & Restore.