What is the difference between shuffle in fit_generator and shuffle in flow_from_directory?
From fit_generator() documentation:


  shuffle: Boolean. Whether to shuffle the order of the batches at the beginning of each epoch. Only used with instances of Sequence
  (keras.utils.Sequence). Has no effect when steps_per_epoch is not
  None.


So if you are using a generator and set steps_per_epoch it would have no effect. In case of using a Sequence generator, it would get the batches in different order at each epoch. For example, in first epoch it might get my_seq[0] and then my_seq[1] and then my_seq[2] (and so on) and in the second epoch it might get my_seq[2] and then my_seq[0] and then my_seq[1] and so on for the next epochs (i.e. note that my_seq[i] is the i-th batch generated by the Sequence generator we have defined).

From flow_from_directory() documentation:


  shuffle: Whether to shuffle the data (default: True)


It is not clear when and how shuffling is done. So we must take a look at the source code. By doing so, we find out that flow_from_directory() method returns an instance of DirectoryIterator class which in its docstring we can see the following:


  shuffle: Boolean, whether to shuffle the data between epochs.


So it would shuffle all of the data (i.e. list of all the training images to be read at each epoch) at the beginning of each epoch.