USPS Flat Rates packaging options are only available to Express Mail and Priority Mail Services.

USPS Flat Rates packaging options are only available to Express Mail and Priority Mail Services.  
Express Mail 
 
1. Flat Rate Envelope
2. Flat Rate Legal Envelope
 
Priority Mail
 
1. Parcel
2. Small Flat Rate Box
3. Medium Flat Rate Box
4. Large Flat Rate Box
5. Flat Rate Envelope
6. Flat Rate Legal Envelope
7. Flat Rate Padded Envelope
8. Flat Rate Gift Card Envelope
9. Flat Rate Window Envelope
10. Flat Rate Cardboard Envelope
11. Small Flat Rate Envelope
If you choose a Flat Rate option for services other than Express Mail and Priority Mail, you will get this warning message:
 

"The Carrier Packaging that you have selected is not valid for this item fulfillment. Usually this indicates the selected packaging cannot be used with the selected USPS shipping method, or the package weight is invalid. Please check the documentation for more details."

 
References:
http://www.usps.com/prices/priority-mail-prices.htm
http://www.usps.com/prices/express-mail-prices.htm