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.
St George’s Day is England’s national day – St George was named as England’s principal patron saint in 1416.
St George’s Day is listed as a flag flying day (for England only) by UK government guidance.
https://www.gov.uk/guidance/designated-days-for-union-flag-flying
The Union Flag is specified.