What's a good way to install a linux distro, from already installed linux distribution?
You can find many guide how to boot ISO by adding a GRUB custom entry. Most of them addresses Ubuntu which uses casper. I have to have a Solus iso. I used an modified entry for CentOS. It booted but initrd-switch-root.service failed, sending me to root shell. Anyway, UNetbootin can write iso to HDD. See this. Make a partition, burn the ISO on that partition using Unetbootin (from Windows, but Linux may work as well). Boot from HDD as Live media and install.