Is charity permissible for a slave, or is his charity considered Zakat for his master?

If you mean, is it permissible for a slave to give charity from his money, then the answer is: it is not permissible except with the permission of his master.

And if you mean, is Zakat obligatory upon the slave for the money he possesses, then the answer is: there is no Zakat upon the slave because his ownership is not complete, and this is the saying of most scholars. And Zakat on his money is not obligatory upon his master according to some scholars.