I am not allowed to comment, so I am adding it here. Not sure I understand, are you asking if the training data must be ordered?
If so, training data must be random, and not AaBbCc or ABCabc. Here the input to the NN will be the source image, and a category 90 degrees or 270 degrees as too separate inputs. i.e. inputs [0...k][k+1][k+2], where 0 - k are normalised pixel data, k+1 is 1 for 90 degree rotation else 0, and k+2 is 1 for 270 degree rotation else 0. Alternatively for more rotation options lets make a = input [k+1] and b = input [k+2]. If a = 0 and b = 0 then 0 degrees, if a = 0 and b = 1 then 90 degrees, if a = 1 and b = 0 then 180 degrees if a = 1 and b = 1 then 270 degrees.
From your image set, draw 3 samples. Sample 1 [training set] must be say 50% of the images, sample 2 [validation set] say 30% of the images and sample 3 [out of sample set] 20% of the images.
Use the training images from sample 1 to update the weights. Read in images from sample 1 at random, the rotation must be random, use your image rotator to rotate the image, and compare it to the output of the neural network, calculate the sum of the mean error and perform gradient descent to update the weights. Repeat the process. After every x weight updates randomly select a few images from the validation set and calculate an error value. If the average error value of the validation images are above some threshold then stop, or if the error begins to get worse. Do not use the validation set to update the weights
At the end use the out-of-sample set of images to verify the performance of the neural network.
The process above does not include hyper-parameter optimisation, or any other optimisation techniques, but does describe the basic way of training a NN using supervised learning.