The most glaring thing is that you're using "dnf". Before Fedora 22, the package manager was "yum". Just drop dnf with yum in your commands and package searches until you're onto 22 or 23, and you should be good to go.
I suspect that for releases that old (<22) that one can use FedUp
https://fedoraproject.org/wiki/FedUp
Also, one can only skip one Fedora release, so you're best to upgrade to 21 or 22, then on to 23. If you're using the KDE Spin, expect your desktop settings to be reset and some major changes with Plasma 5 in 22 & 23.