Hi Before upgrading
1) Take SQL Backups of ReportServer and ResportServerTempDB
2) Connect to SSRS through via InternetExplorer and take backups of Encryption keys with password
3) Once the SQL Server 2016 installed
4) Restore the SQL Backups of 2012 from step 1
5) Configure SSRS to use with existing restored databases ( 2012 databases)
6) Restore encryption key from step 2
7) Restart the SQL SSRS services
https://www.mssqltips.com/sqlservertip/2692/migrating-sql-reporting-services-to-a-new-server-by-moving-the-reporting-services-databases/
Before doing please test this setups....
Thanks, Satish Kumar. Please mark as this post as answered if my anser helps you to resolves your issue :)