The birthday of the Princess Royal 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/
Montmouthshire Day takes place each year on 25 September, the feast of Saint Cadoc or Cadog (born c. 497).
Cadoc was the founder of the monastery of Llancarfan, and a pioneer of Celtic Christianity in Wales.
Caernarfonshire Day takes place annually on 28 November.
It commemorates the death of Prince Owain Gwynedd, King of Gwynedd (1137–70).
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/
St David’s Day is Wales’ national day.
The Senedd Cymru flies the Welsh national flag – Y Ddraig Goch (The Red Dragon) – all year round.
On St David’s Day it also flies the flag of St David (below).
https://senedd.wales/media/hl5dtuct/foi-574-final-redacted-response-saes.pdf
St David’s Day is also listed as a flag flying day (for Wales only) by UK government guidance.
The Union Flag is specified.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
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/
St Patrick’s Day is listed as a flag flying day (for Northern Ireland only) by UK government guidance.
The Union Flag is specified.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
There is no official, current pan-Ireland or Northern Ireland flag that may be used to mark St Patrick’s Day.
St Patrick’s Saltire is one of several possible alternatives.
The birthday of the Duke of Rothesay (Prince of Wales) is 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 Prince of Wales is also 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