I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are sparse.
For Michael Flynn B 1825 +/- 1 yr in Westmeath or Meath, I found 1 B rcd in 1826 Westmeath.
For Michael Flynn M 1860 +/- 2 yrs, I found 2 M rcds: 1858 & 1861. Both are in Co. Meath. A view of the M rcds SHOULD show the spouse's name. This will validate/invalidate the rcd.
For Joseph Flynn B 1862 +/- 1 yr, I found 0 B rcds in either Meath or Westmeath.
For Thomas Flynn B 1866 +/- 1 yr, I found 2 B rcds: 1865 & 1866 in Meath.
For the children B after 1863, B/M/D registration was civil. Their B rcds are kept by the General Register Office. Visit its website at http://www.groireland.iehttp://www.groireland.ie to ask for copies. The copies should reveal more info abt the family's history such as mother's maiden name, residence, etc.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.