A check for original copyright registrations under artwork was done for the year 1936. There were only 2 photos registered by Associated Press and neither pertained to the Hindenburg. There's no evidence that copyright was registered for this photo.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.