Your purchased themes and content are all backed up to your SwiftKey Account. Just as apps you download from Google Play are assigned to a Google account, your SwiftKey Keyboard content works the same way.
When you download SwiftKey Keyboard on your new phone, be sure to sign into the same SwiftKey Account that you used to purchase your content from the SwiftKey Store. Your purchased themes should show as available to download.
Note: All SwiftKey themes are now available free of charge. Read more here.