(still under USN jurisdiction)
Lt F.-
Not quite sure where you got that bit, but the rest is pretty much correct so far as I can tell. In general, the USCG only has gone under USN control during time of war and did so in 1941, having been returned to the Treasury Department (its then home) in 1916 after WWI. As far as I am aware, it wasn't done between the wars nor since WWII. They probably would have told me if it had.
The Coast Guard hangar at Dinner Key is still there (was once based in Miami, then (and probably yet) the busiest air-sea rescue unit in the world, but Dinner Key had closed some years prior), and the business that now owns the hangar has been good enough to paint the embossed concrete CG emblem over the doors in CG colors. The seaplane ramp was even there some years back, though it was launching pleasure craft. May still be for all I know.
Since the famous picture of Orville Wright sailing off on his first powered flight was taken by Surfman John T. Daniels from the Kill Devil Hills Life Saving Station, arguably the USCG has been there from the start.
It also isn't entirely clear when CG aviation SAR began, but I think you're in the general timeframe. CG Aviator #1 was Elmer Stone, and he went to the Naval Aviation School in Pensacola in April 1916. There were some abortive starts of air stations in 1916 and 1920.
The first trans-atlantic flight of a heavier-than-air craft was in May, 1919, in the NC-4. LT Elmer F. Stone USCG first pilot, LCDR A. C. Read USN, aircraft captain.
In 1925 LCDR C.G. von Paulsen borrowed a Vought UO-1 from the Navy (things were easier then, apparently) to demonstrate the use of aircraft in enforcing Prohibition. So, law enforcement was the first real USCG aviation mission.
The earliest date I can find for aviation SAR for the USCG is around 1928, flying PJ-1s and Grumman JF-2 Ducks were based aboard ship by the late 1930s. There were some crazy missions capturing German weather stations in Greenland during the war and numerous rescue missions of ferry crews who'd crashed on the ice cap. I don't know how well any of that is documented, as my history book on it is somewhat disorganized and vague (
History of U.S. Coast Guard Aviation by Arthur Pearcy... who is a British fellow, so highly credible... also he's one of the few who bothered to write anything at all... though his book is now 20 years old so the contemporary bits are off now).
What little helicopter training was done by the Allies during WWII was all done at Brooklyn, NY, by the USCG (who controlled almost all U.S. Naval helicopters during that time), though the British were indeed there for the start of things with helicopters around February, 1943. In November 1943, shipboard helicopter trials were conducted in Long Island Sound with two YR-4B helicopters, one U.S. Navy, one Royal Navy. On 2 January 1944, the British Helicopter Service Trial Unit embarked aboard the merchant vessel
Daghestan at Bridgeport, Connecticut with two helicopters. The ship proceeded to New York where USCG and USN observers boarded. The ship joined a convoy on 6 January for Liverpool, which apparently was eventful for weather and a couple of short flights mid-Atlantic. Apparently there were wartime helicopter rescue missions completed in Burma. While my reference doesn't say who flew those, one would think it was the British.
There were plenty of strange machines along the entire way, including 18 B-17s which were acquired from the USAF in 1945 which had lifeboats fitted to the belly.
The point of this enormous post is that it doesn't really matter who did what first. In many cases the documentation seems to be so poor that no one really knows anyway. The point is that the history of airborne SAR is one of inventiveness, adaptation, and shameless borrowing from one another. Long may it continue.