All military personnel during World War II were granted "free" mailing privileges and as evidenced by your example, all the soldier or sailor had to do was write "Free" in the upper right hand corner of the piece and it would be honored in lieu of a stamp. The idea was that the mails were so important to deployed troops that it became a morale booster for the soldier and their families to communicate while at war.
Here's a WWII-era newspaper article announcing the program, which became effective April 1, 1942:
