We like to let all our moms know that TSA is very likely to do special inspections on the coolers - specifically the cooling units inside - since they don't see them every day and and may be curious. The cooling units use evaporation technology and don't contain any hazardous materials like dry ice - which is usually their main concern.
Be prepared and allow extra time for TSA inspection. Just know that you are not required to put your breast milk through the X-ray machine, but YOU AND YOUR LUGGAGE WILL BE SUBJECT TO ADDITIONAL SCREENING.
A couple valuable resources are:
Milk Stork's Airport Security Guide