There are two ways to move your account. Discord is the easiest. A transfer code works too.
With Discord (easiest)
Make sure Discord is linked.
On the old phone, open Other > Account. The page shows Discord: linked. Not linked yet? Follow Link your account to Discord.
Install the app on the new phone.
Use the Download page.
Sign in with Discord.
Open the game and tap Sign in with Discord on the title screen notice, using the same Discord account. Your account moves to the new phone and the old phone is signed out.
With a transfer code
Find your code on the old phone.
Open Other > Data Transfer. Write down your User ID and your Transfer Code (16 letters and numbers).
Install the app on the new phone.
Use the Download page.
Open Data Transfer on the new phone.
On the title screen, tap Data Transfer.
Enter both.
Type your User ID and your Transfer Code. Your account moves to the new phone and the old phone is signed out.
Reinstalling on the same phone
Uninstalling the app or clearing its data signs this phone out of your account. Before you do it, link Discord or write down your User ID and Transfer Code. Then, after the reinstall, tap Sign in with Discord on the title screen notice, or use Data Transfer on the title screen.
Checked against the live game on .