The Falkland Islands celebrate Liberation Day annually on 14 June.
The date commemorates the liberation of the islands from Argentine military occupation in 1982.
Sussex Day takes place annually on 16 June, the feast of St Richard of Chichester (1197–1253), the patron saint of Sussex.
Also known as Richard de Wych, the saint was bishop of Chichester.
Autistic Pride Day 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 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
Shetland Day takes place annually on 21 June.
Shetland Islands Council chose this date simply because it it the longest day of the year.
Suffolk Day takes place annually on 21 June.
Former BBC radio presenter Mark Murphy created the event in 2016.
It has since become a staple in the Suffolk calendar, hosted by towns across the county.
Mercia Day takes place annually on 22 June, the feast of St Alban.
St Alban is the first recorded British Christian martyr, by tradition beheaded in Verulamium (modern St Albans) during the third or fourth centuries.
Armed Forces Day takes place each year on the last Saturday in June.
It is an official flag flying day in Scotland.
https://www.gov.scot/publications/flag-flying-on-government-buildings/
The UK government does not designate it as an official flag flying day in the rest of the UK.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
However the Senedd Cymru flies the Armed Forces Day flag on 24 June and throughout the preceding week.
https://senedd.wales/media/hl5dtuct/foi-574-final-redacted-response-saes.pdf
The British Virgin Islands celebrate Territory Day annually on 1 July.
On this date in 1956 the islands became a separate British Overseas Territory.
The Cayman Islands celebrate Constitution Day on the first Monday of July.
It honours the island’s first written constitution, which took effect on 4 July 1959.