Viet Nam People's Air Force (Vietnamese: Không quân Nhân dân Việt Nam, KQ-PKKQ) (Air Force Viet Nam-Air Defence) or more commonly Vietnamese Air Force or Vietnamese People's Air Force) is a Branch within the Viet Nam People's Army and part of the Air Force-Air Defense dual command. It was established in 1959 with the creation of the first squadrons, but dates back its roots to 9 March 1949 when General Vo Nguyen Giap was authorised to establish the Air Force Research Committee (Ban Nghiên cứu Không quân) under the General Staff to study ways to deal with the air war.
Source: Wikipedia article Esteban Rivera, 13 February 2016
Looking at some information on the Vietnam Military History Museum (Bảo tàng Lịch sử Quân sự Việt Nam) official website (http://www.btlsqsvn.org.vn/?act=mn_index&lgid=2), one can find the following image: http://www.btlsqsvn.org.vn/images/upload/Image/54-68-7.jpg.
As the link mentions (http://btlsqsvn.org.vn/showid.php?id=2471) "It is the Best Unit” flag awarded to Company 1, Regiment 921 of the Vietnam People’s Air Force for their feat of arms in 1965."
I believe they refer to an action where the Regiment 921 Sao Do (Sao Đỏ) (translates as Red Star) of the VPAF (Vietnamese People's Air Force) (Không Quân Nhân Dân Việt Nam) was responsible for the first jet air-to-air engagement with U.S. aircraft, which was on April 3, 1965. The VPAF claimed the shooting down of one US Navy F-8 Crusader, which was not confirmed by US sources, although they acknowledged having encountered MiGs. Consequently, April 3rd became "North Vietnamese Air Force Day". On April 4 the VPAF (NVAF) scored the first confirmed victories to be acknowledged by both sides. The US fighter community was shocked when relatively slow, post-Korean era MiG-17 fighters shot down advanced F-105 Thunderchief fighter-bombers attacking the Thanh Hoa Bridge, known by locals as Ham Rong (Dragon's jaw). The two downed F-105s were carrying their normal heavy bomb load, and were not able to react to their attackers. In their first air combat, a small force of seemingly mismatched MiG-17s inflicted significant losses on much larger and more advanced American F-105 Thunderchief and F-8 Crusader fighters at a cost of 3 of their own, with an F-100 Super Sabre claiming the first probable American kill of the conflict. This would lead to significant changes in American tactics, training and fighter design, and a return to dogfighting in air combat doctrine. This took place during the Operation ROLLING THUNDER, an aerial bombardment campaign from 2 March 1965 to 1 November 1968. On the 45th anniversary of the Battle in 2010, Vietnam celebrated the downing of 47 U.S. aircraft. (Notice that the Air Force was an "Arm" of the Army at the time)
It is also important to mention that this was not the first shootdown of the VPAF. The first shootdown took place 16 February 1964, when a T-28 "Trojan" (piloted by a Thai who had defected in Septmeber 1963) shot down a C-123 "Provider", of the VNAF (Viet Nam Air Force, Không Quân Việt Nam).