How to get feature importance from RandomForest using scikit-multilearn library?
First, to directly answer your question, the easiest way to get Feature Importance using scikit learn is this, where model is the variable holding your classifier.

print(model.feature_importances_)


However, this method only exists on some of the Ensemble models, namely:


AdaBoostClassifier
AdaBoostRegressor
ExtraTreesClassifier
ExtraTreesRegressor
GradientBoostingClassifer
GradientBoostingRegressor
RandomForestClassifier
RandomForestRegressor
RandomTreesEmbedding


If you're wondering why, there's a fantastic free book online all about Interpretable Machine Learning. Here's an excerpt:


  The easiest way to achieve interpretability is to use only a subset of
  algorithms that create interpretable models. Linear regression,
  logistic regression and the decision tree are commonly used
  interpretable models.


Once you've chosen the right model, beware of using feature importance! See here, it ranks random data very highly. The article proposes using Permutation Importance instead, as well as Drop-Column Importance.

They created a library called rfpimp for doing this, but here's a tutorial from scikit themselves on how to do both of those with just scikit-learn. I've pasted the permutation importance example from that tutorial below:

from sklearn.inspection import permutation_importance

result = permutation_importance(rf, X_test, y_test, n_repeats=10,
                                random_state=42, n_jobs=2)
sorted_idx = result.importances_mean.argsort()

fig, ax = plt.subplots()
ax.boxplot(result.importances[sorted_idx].T,
           vert=False, labels=X_test.columns[sorted_idx])
ax.set_title("Permutation Importances (test set)")
fig.tight_layout()
plt.show()