The reason is slaves needed a stick for rice - putting a chain between two stick sill works fine for rice work - but makes it a much worse weapon.

That reasoning makes no sense. There was no significant production of rice by slaves.

But also, threshing flails were used outside of rice-growing regions.

https://upload.wikimedia.org/wikipedia/commons/8/81/Battage_...

Considering that they must be hundreds of times more expensive than long sticks with no hinge, I would say the reason must be that they're better at threshing.