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Dear Mr. Weber,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located 17 series that pertain to the Distinguished Flying Cross (DFC). Please review the series listed. Once you have determined which series may contain the information you seek, please contact the reference unit listed in the series description. Most awards are recorded in the general orders of the unit or command approving the award. The U.S. Navy, the U.S. Army, and the U.S. Army Air Corps awarded the DFC.
We also checked several non-official websites such as Recipients of the Distinguished Flying Cross (United States); The Distinguished Flying Cross Society; and the Wall of Valor - Distinguished Flying Cross Recipients but a R.D.Berning was not listed.
We hope this information is helpful. Best of luck with your research!