The Irish Family History Foundation's database accepts O'Flynn and Flynn (plus other variants) as being the same.
Since your ancestors seem to have been in the Royal Navy, this means that rcds for them likely exist in the UK National Archives. Suggest you try there.
For your Great uncle George, search naturalization papers for the decade following his arrival in the U.S. George is a rarely used forename with an Irish surname. This search will likely give you an address. From there, look for census records for the relevant decades.
George is likely deceased by now. However, he would have paid into the Social Securtiy fund. Search the Social Security Death Index (SSDI) online for his name. This should give you the address to which his Social Security Benefits were sent at the time of his death.