In 1943 JG 1 had a checkerboard or a B/W striping on their Fw 190s - until it was realized that the Allies were using a similar pattern on their P-47s and flak units couldn't tell the difference. Don't know off the top of my head if any were shot down but it did demand a change of markings for the Jagdgeschwader.
9/7/44 Lt Jack B. Miller 78thFG shot down by Spitfire
9/7/44 Spitfire PL137 shot down by P-47 353rdFG
14/7/44 Mitchell 226 Sqn shot down Mosquito
15/8/44 Two Spits 602 Sqn (MJ398 and MK244) shot down by P-51s
26/8/44 Spit 602 Sqn (PL264) shot down by P-47
18/9/44 Lt Robert O. Peters 335thFG shot down by P-51
19/9/44 P-51 357thFG shot down by Spitfire
26/9/44 Mustang 168 Sqn (AM101) shot down by P-47
7/10/44 Lt Raoul Rebiere 328 Sqn shot down P-51
10 Sept 43 Lt. Pryblo 307th FS 31st FG-- Own Flak
22 May 44 Nick "Cowboy" Megura 334th FS-- 4th FG Shot down by P-38
6 June 44 Uffz. Winter 6./JG 26-- Own Flak
25 December Lt. Bouchier-- Own Flak
25 December Capt. Don Emmerson 336 FS 4th FG-- Own Flak
1 Jan 45 An RAF Typhoon or Tempest was shot down and the pilot KIA while in the landing pattern by a pilot from the 328th FS 352nd FG at Y-29 in Belgium.
1 Jan 45 out of about 300 aircraft lost by the Luftwaffe during Operation Bodenplatte about 100 were shot down by their own flak.
ad infinitum there s a ton of them I'm even aware of a Lanc shooting down a lanc in 45