If you want to make sure that there is any leftover, try to run this in terminal
sudo apt purge --auto-remove retroarch
After that, remove the ppa repo from the lists, and do an apt update
Now for the flatpak. I assure that you are using a version of Linux Mint above 18.3, right? If so, just open the terminal and then:
flatpak install retroarch
Press Y to confirm. This will install RA and a lot of dependencies. No worries, that’s normal and take more time and space then a normal install.