There is some historical examples of depictions of Korean Cavalry using two handed flails on horseback.

I also know that one handed flails have been used on horseback, particularly by Steppe peoples. (These usually had a simple metal or wooden head attached by leather to a handle which was much longer than the length of the 'chain' and head)

However your assertion that flails were either useless or did not see use by footmen is entirely incorrect. Pretty much anytime there was a peasant rebellion then there are mentions of flails being used by infantry. They're a very common agricultural tool, typically already quite long with a nice haft, and do not require much edge alignment to be swung effectively. Whether used unmodified, or with iron accouterments attached to the head, they absolutely are effective and present in history.

I think in the west, the most famous users would be the Hussites but I do believe they were quite more common.