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 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/
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 Duchess of Edinburgh (and Countess of Forfar) 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 start of LGBT+ History Month 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 Duke of Edinburgh (and Earl of Forfar) 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/
Commonwealth Day is the second Monday in March.
The UK government states that the Union Flag should be flown.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
The Scottish government states that the Commonwealth flag should be flown.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
The Senedd Cymru states that the Commonwealth flag should be flown.
https://senedd.wales/media/hl5dtuct/foi-574-final-redacted-response-saes.pdf
International Workers’ Memorial Day is a day of remembrance and action for workers killed, disabled, injured, or made unwell by their work.
It is an official flag flying day only in Scotland, not in the rest of the UK.
The saltire(s) should be hoisted right up and then lowered to half-mast for the day.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
The Coronation Day 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 Coronation Day 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/
Europe Day is celebrated annually on 5 May and 9 May.
The European Union designates 9 May, the anniversary of the Schuman Declaration (1950).
https://european-union.europa.eu/principles-countries-history/symbols/europe-day_en
The Council of Europe designates 5 May, the anniversary of the Council’s founding.
https://www.coe.int/en/web/portal/5-may-europe-day
Europe Day is listed on 9 May as a flag flying day by Scottish government guidance.
The European Flag is specified.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
Neither date is listed as a flag flying day by UK government guidance, although the UK remains a member of the Council of Europe.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying