This is the Council of Europe’s day, rather than the EU day which is on the 9th May. The United Kingdom is a full member of the Council of Europe.
The county day was chosen as part of a vote. The other options in the vote can be considered to be other particularly appropriate dates on which the Somerset flag can be flown. These include:
19th May – St Dunstan’s feast day
6th July – The battle of Sedgmoor