Tools that take a kinship matrix for phylogenetic decorrelation
If you willing to do Bayesian model fitting, this is likely possible but will take some tinkering to make sure the models are what you think they are. Stan (via rstan or brms), can fit multinomial logistic regressions (A demo from Thinkinator).

If you can convert these models to pure stan code, then you can incorporate phylogenetic/kinship/arbitrary correlation structure into the model following this example on github (or this one). I have had better luck getting phylogenetic regression to work correctly in pure stan than via convenience functions.