First, open a file manager and navigate to main storage > android > data > com.r3nn.ld > files. Copy the "saves" folder and "log.txt" files. Next, paste and upload them to a cloud storage service like Google Drive (make sure you have all the necessary account details).
When setting up your new phone, install the same file manager. Log in to your Google Drive account there to access the uploaded files. Copy the "saves" folder and "log.txt" from the drive, then navigate to main storage > android > data > com.r3nn.ld > files on the new phone. Replace the existing "saves" file with the copies you just made.
Or simply just use a flash drive if you have one.