UK Government guidelines state that the Union Flag should be flown on Remembrance Sunday (the second Sunday in November).
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
Scottish government guidance also lists Remembrance Sunday as a flag flying day.
The Union Flag is specified.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
The Royal British Legion recommends flying the Union Flag on Remembrance Day (11 November) and Remembrance Sunday.
https://support.britishlegion.org.uk/app/answers/detail/a_id/263/~/remembrance-faqs
The flag should not be flown at half mast on either day.
The British Antarctic Territory celebrates the Birthday of HM The King annually on 14 November.
The Falkland Islands celebrate the Birthday of HM The King annually on 14 November.
The Birthday of HM The King is listed as a flag flying day by UK government guidance.
The Union Flag is specified.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
The Birthday of HM The King is also listed as a flag flying day by Scottish government guidance.
The Scottish Saltire is specified.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
Lancashire Day has taken place annually on 27 November since 1996.
It commemorates the day when Lancashire first sent representatives to Parliament, the Model Parliament of King Edward I (1295).
Bedfordshire Day takes place annually on 28 November.
The date, chosen by popular vote, commemorates the birthday of John Bunyan.
Several alternative options included:19 January – earldom (later dukedom) of Bedford recreated (1550); 12 April – Bedfordshire County Council granted its coat-of-arms (1951); 20 June – siege of Bedford Castle begins (1224); 13 August – Blenheim Day, celebrated by the Bedfordshire Regiment and its successors; 12 September – birth of prison reformer John Howard (1726); 14 October – first flight of the airship R101 from Cardington (1929); 6 November – 1st and 2nd Battalions Bedfordshire Regiment meet at Bailleul en route to Ypres (1914); 15 November – first High Sheriff of Bedfordshire appointed (1575); 25 November – feast of St Catherine, patron saint of spinners, weavers and lacemakers; 15 December – birth of Olympic athlete Harold Abrahams (1899).
Caernarfonshire Day takes place annually on 28 November.
It commemorates the death of Prince Owain Gwynedd, King of Gwynedd (1137–70).
Alderney celebrates Homecoming Day annually on 15 December.
The people of Alderney were evacuated in June 1940 before the German occupation.
Homecoming Day marks the day the islanders could first return home in 1945.
The birthday of the Duchess of Rothesay (Princess of Wales) is an official flag flying day only in Scotland, not in the rest of the UK.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
The birthday of the Countess of Forfar (Duchess of Edinburgh) is an official flag flying day only in Scotland, not in the rest of the UK.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
