Your purchased themes and content are all backed up to your Microsoft SwiftKey Account.
When you download Microsoft SwiftKey Keyboard on your new phone or your other Android devices, be sure to sign into the same Microsoft SwiftKey Account that you used to purchase your content from the SwiftKey Theme Store. Your purchased themes should show as available to download.
Please note that themes cannot be synced across Android/iOS platforms.
Also, please note that it is not currently possible to use Backup & Sync to save your Photo themes to your Microsoft SwiftKey Account.