1. The Joker is telling, surprise surprise, a joke. The expectation is that two evil villains will team up because they're both evil villains, and the punch line is that somehow THIS is where the Joker draws the line. The Joker always does what is funniest at the time, based on his own twisted sense of humor. In this case, not joining with the Red Skull is funnier than joining him.
2. Anyone who thinks that the Joker would be a 'good fascist' doesn't know what Fascism means, and doesn't understand the Joker either.
Fascism is an AUTHORITARIAN MILITARIST NATIONALIST political ideology which advocates that - instead of hanging all the rich from trees in order to redistribute the means of production and solve social inequality - the state and corporate class works together through an 'organic' (which is to say, with parts that are like organs to a body; government = brain, populace = various cells) economy. Among other things, of course, but that's the bread and butter of fascism. The mundane stuff.
And oh by the way, the Joker is INSANE.
Does he really sound like someone into hierarchical militarism, socialist populism, and central planning?
Really the Joker isn't even an anarchist. He isn't an '-ist' at all.