Terri:
Welcome to Ireland Reaching Out!
I did some searching and found the following information. First two links are the 1901 and 1911 census records for the family. In 1901 and 1911 Timothy and Bridget were in Ballyderown townland in Kilcrumper civil parish. Timothy died in December 1903 so Bridget was living alone in Ballyderown in 1911. I looked for Bridget's death record. It appears she died in 1917 but the image was the wrong image.
From what I can see on Roots Ireland, the maiden name for the mother Bridget was either Swayne or Savage. The baptismal record transcription for Patrick shows Swayne but other records show Savage and I also located a possible marriage record in Kilworth for Timothy Flynn and Bridget Savage.
I would suggest that you get a short-term subscription to Roots Ireland and search for the baptismal transcriptions for the children. I found fifteen Flynn baptismal record transcriptions where the father was Timothy and the mother was Bridget.
The records below are as follows: 1901 and 1911 censuses, Civil death record for Timothy (you will have to sign-in to see the record), parish registers for Conna and Kilworth, transcription of Patrick's baptismal record and finally a transcription of a potential marriage record.
Let me know what questions you have.
Roger McDonnell
http://census.nationalarchives.ie/pages/1901/Cork/Kilworth/Ballyderown/…
http://census.nationalarchives.ie/pages/1911/Cork/Kilworth/Ballyderown/…
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
http://registers.nli.ie/parishes/0072 http://registers.nli.ie/parishes/0037
Name:Patrick FlynnDate of Birth:
Date of Baptism:16-Mar-1860Address:BallybrideParish/District:CONNAGender:MaleCountyCo. Cork
Denomination:Roman Catholic
Father:Timothy FlynnMother:Bridget SwayneOccupation:
Sponsor 1 /
Informant 1:Michael Beecher Sponsor 2 /
Informant 2:Mary Barrett
Date of Marriage:11-Feb-1844
Parish / District:KILWORTH
County:Co. Cork
Husband TimothyFlynn
Wife BridgetSavage