Firstly, Random Forest / Xgboost or even a simple DecisionTree/ any Tree ensemble is a inherent multi-class classification model. Hence it will predict the multi-class output without using any wrapper ( 1 vs 1 / 1 vs Rest) on top of binary classifier (which is what the logistic regression/SVM/SGDClassifier would do).
Hence, you can get the feature importance for the overall multi-class classification alone and not for individual labels.
If you really want to know the feature importance for individual labels, then use onevsRest wrapper with decisionTree/ RandomForest/ Xgboost as the estimator.
This is not the recommended approach because the results could be suboptimal when compared with single decision Tree.
Some examples here.