Don't know if anyone has mentioned these (or if they were truly Flag Carriers) but, using the Carrier Decode list from the BTS I find (Excel file attached):

CARRIER CARRIER_NAME START_DATE_SOURCE THRU_DATE_SOURCE AJ Air Micronesia Inc. 7/1/1981 12/31/1989 IR Iran National Airlines Corp 1/1/1995 12/31/2000 RB Syrian Arab Airlines 5/1/1996 12/31/2014 ST Belize Airways Limited 7/1/1981 12/31/1989 UMQ Air Manila Inc. 4/1/1994 5/31/1996 WM Windward Islands Airways 7/1/1981 9/30/1993 JU Yugoslav Airlines 1/1/1986 7/31/1996 SZQ Aerolineas El Salvador S A 1/1/2013 12/31/2020 ADQ Aeronaves Del Peru 11/1/1996 7/31/1997 WT Nigeria Airways Ltd. 11/1/1996 7/31/2010 VA Venezuelan International Airways 7/1/1981 12/31/1996 CP Canadian Airlines International Ltd. 1/1/1997 8/31/2001 GY Guyana Airways Corporation 1/1/1997 10/31/2001 AI Air-India 3/1/1997 10/31/2000 AM Aeromexico 7/1/1981 12/31/1989 AR Aerolineas Argentinas 5/1/1992 2/28/1997 AV Aerovias Nacl De Colombia 5/1/1997 11/30/1997 CA Air China 11/1/1997 9/30/2001 FI Icelandair 12/1/1991 1/31/1993 IB Iberia Air Lines Of Spain 1/1/1998 1/31/2001 JL Japan Air Lines Co. Ltd. 3/1/1996 12/31/1997 JM Air Jamaica Limited 1/1/1998 5/31/2001 KE Korean Air Lines Co. Ltd. 3/1/1996 12/31/1997 KL Klm Royal Dutch Airlines 10/1/1995 12/31/1997 LA Lan-Chile Airlines 1/1/1998 9/30/2005 LY El Al Israel Airlines Ltd. 1/1/2010 3/31/2017 MX Compania Mexicana De Aviaci 1/1/1998 12/31/2005 OA Olympic Airways 1/1/1987 12/31/1997 PH Polynesian Airlines Ltd. 4/1/1998 4/30/2004 PK Pakistan International Airlines 10/1/1987 12/31/1988 PR Philippine Airlines Inc. 10/1/1987 3/31/1998 PY Surinam Airways Limited 4/1/1998 12/31/2006 RO Tarom Romanian Air Transpor 7/1/1998 6/30/2017 SA South African Airways 1/1/1990 7/31/1994 SK Scandinavian Airlines Sys. 7/1/1998 2/29/2008 SU Aeroflot Russian Airlines 9/1/1998 11/30/1998 TA Taca International Airlines 11/1/1998 7/31/1999 TP Tap-Portuguese Airlines 12/1/1998 4/30/2001 UP Bahamasair Holding Limited 12/1/1998 10/31/2000 EOQ Aeroservicios Ecuatorianos 1/1/2000 9/30/2010 KU Kuwait Airways Corp. 1/1/2011 12/31/2011 EI Aer Lingus Plc 1/1/2007 12/31/2013 SV Saudi Arabian Airlines Corp 1/1/2001 12/31/2006 CIQ A/S Conair 1/1/2001 12/31/2006 MB Samoa Airlines Inc. 4/1/1996 12/31/2002 KB Haiti Air 7/1/1986 9/30/1987 MS Egyptair 1/1/2011 6/30/2012 NH All Nippon Airways Co. 4/1/1997 6/30/1998 MH Malaysian Airline System 4/1/2004 12/31/2004 GG Grenada Airways Ltd. 3/1/1994 9/30/2002 Q2 Zambia Airways Corp. 1/1/2005 12/31/2006 KA Hong Kong Dragonair 4/1/2006 12/31/2007 4H Belize Trans Air 2/1/2007 2/29/2012 UYQ Aerolineas Uruguayas S.A. 9/1/2018 3/31/2020

I'm pretty sure a number of these reincorporated and are probably wrong. I just filtered for and end date and selected ones with National Sounding Names. The entire list can be found here: BTS Transtats