But the post was about the countries OWNING an airline. Scotland does not own Loganair. Ireland via the government does own 25% of Aer Lingus. The Country of Wales does NOT OWN Air Wales. England does NOt own BA since it was privatised in the 1980's so the often used term "flag carrier" is wrong. Guernsey does of course own Aurigney.
If you actually mean the main carrier in a country then Easyjet for Northern Ireland, maybe Ryanair for the UK and Ireland and Easyjet also for Wales.