Probably the real reason you cant turn the nut on the flush handle is because toilet flush handle mount nuts are reverse threads. Turn it the opposite direction you would normally turn an nut.
You should be able to hold the handle steady with a pair of channel lock pliers, then turn the nut with a second pair of channel locks or an adjustable wrench.
Most of the nuts are made of a cheap pot metal and if it won't turn off, the nut should break fairly easy.
If you can't get it off that way, you can cut the nut with a mini-hacksaw.
