ICAO airline codes are 3 digit alphabetical codes (BAW, AFR, FCA, EZY, MON). From a passenger perspective, airlines generally choose whichever code they think passengers will remember; however, most flight plans would use the 3 digit ICAO codes.
For a list of codes, see here.
All flight plans run on the 3 letter codes, or aircraft registration, you cant use the 2 letter for this purpose