Have you tried the Irish Heritage Centre in Clare? Seeing that you know your gr grandfather was George Patrick Flanagan and he came from Ennistymon and arrived in the USA in 1898 and his family still lived at Ennistymon in 1922, you should be able to trace how long the family lived in the district.
This would give you some vital information about the family unit and possibly occupations associated with it through associated births and weddings.
As to the RIC, it was a voluntary police service not a conscripted one.
People left Ireland for many reasons - most to better themselves - but I doubt that many were 'deserters' from the RIC which up until the 20th century (Irish war of independence) was a well paid job.
Only after the IRA began killing members of the RIC did some of its members quit the service but that would have ben much later than when your gr grandfather arrived in the USA.
The uniform could have been a military one or a local militia. Try and find it again!