I have found in my searches that the name Bryan/Bernard were interchangable at one point.
That is not to say all Bryan's are Bernards or visa versa but it is possible.
There is a marriage of a Bernard FLYNN in Bullaun/Grange to a Mary ? (I cannot work out the surname) in 1834 on rootsireland.ie;
there are also two FLYNN births to these parents - John 1838 and Cecelia 1835 which is interesting as your John named a daughter Cecelia.
It is possible that for a census someone could be described as a labourer when in fact they have a trade.
This
link shows a search for all FLYNNs in Bullaun which indicates there were at least six contemporaries of your John,
another John x2, Darby, Thomas x2 and Patt all having family baptised in the parish in the 1860's and 1870s.
There are no obvious matches in the 1901 census when they would all have been late in their 60s.
By the way ages were relative to memory or requirement!