Here is the relevant section of the DMM (domestic mail manual) - the BIBLE of the USPS. Print it out and bring it to your local PO if they give you a problem.
And, I repeat, get the new FR padded envelopes.
1.5 Flat Rate Envelopes and Boxes
Any amount of material (up to 70 pounds) may be mailed in a USPS-produced Priority Mail Flat Rate Envelope or Flat Rate Box. When sealing a Flat Rate Envelope or Flat Rate Box, the container flaps must be able to close within the normal folds. Tape may be applied to the flaps and seams to reinforce the container, provided the design of the container is not enlarged by opening the sides and the container is not reconstructed in any way.