Correlations of feature columns in TensorFlow
Tensorflow does not provide the feature_importance feature with the way Sklearn provides for XGBoost.
However, you could do this to test the importance or correlation of your feature with the target feature in TensorFlow as follows.
1) Shuffle the values of the particular feature whose correlation with the target feature you want to test. As in, if your feature is say fea1,the value at df['fea1'][0] becomes the value df['fea1'][4], the value at df['fea1'][2] becomes the value df['fea1'][3] and so on.
2) Now fit the model to your modified training data and check the accuracy with validation data.
3) Now if your accuracy goes down drastically, it means your feature had a high correlation with the target feature, else if the accuracy didn't vary much, it means the feature isn't of great importance (high error = high importance).
You can do the same with other features you introduced to your training data.
This could take some time and effort.
I've recently started exploring for myself features columns by TensorFlow. 
If I understood documentation right, feature columns are just a 'frame' for further transformations just before fitting data to the model. So, if I want to use it, I define some feature columns, create DenseFeatures layer from them, and when I fit data into a model, all features go through that DenseFeatures layer, transforms and then fits into first Dense layer of my NN.
My question is that is it possible at all somehow check correlations of transformed features to my target variable? 
For example, I have a categorical feature, which corresponds to a day of a week (Mon/Tue.../Sun) (say, I change it to 1/2..7). Correlation of it to my target feature will not be the same as correlation of categorical feature column (f.e. indicator),  as a model don't understand that 7 is the maximum of the possible sequence, but in case of categories, it will be a one-hot encoded feature with precise borders.
Let me know if all is clear.
Will be grateful for the help!