When you download SwiftKey Keyboard on your new phone, be sure to sign into the same SwiftKey Cloud account that you used to purchase your content from the SwiftKey Store.
If you need help signing into SwiftKey Cloud, see those instructions here:
Once you are signed in to SwiftKey Cloud, you can enter the Themes page from Settings or by pressing and holding the SwiftKey logo on the bottom left of the keyboard. There, you’ll see all of your previously purchased content that is ready to download.
See the how-to video or images below: