According to the reference book U.S. Army Patches, Flashes and Ovals: An Illustrated Encyclopedia of Cloth Unit Insignia by Barry Jason Stein, the flash and oval here were designated for Company F, 425th Infantry Regiment and were worn beginning on 27 December 1984; whether or not this was the date of approval from The Institute of Heraldry is not clear.
Stein also lists the Company as a Long Range Surveillance (LRS) Ranger unit, which means the 425th Infantry Regiment, Company F flash is worn centered on the stiffener of the tan beret. Officers place their non-subdued insignia of grade on the flash, while NCOs and Junior Enlisted Soldiers wear the 425th Infantry Regiment Distinctive Unit Insignia, also called a unit crest or a DUI. (Note: Our
425th Infantry Regiment DUI page has a concise history of the Regiment and Company F.)
The oval, or background trimming, is worn underneath an authorized Parachutist or Air Assault Badge, with the combination of the two counting as one device/insignia for calculating maximum allowable devices and for measuring purpose to determine placement. It is worn on the Coat of the AGSU, the blue ASU (and its Dress variation), Service Uniform shirts, and the green or blue Army Maternity Tunic (female Soldiers only).
The 425th Infantry Regiment was inactivated in 2011.