This site has Arthur's mother as Frances D FLYNN. (There is a FLYNN listed as a witness at their marriage).

http://pconno.gotdns.com/GenE/dat46.htm
Family Connolly - Flynn

Connolly, Daniel
Gender: Male

Flynn, Frances D.
Gender: Female


Connolly, Arthur Kellogg
Gender: Male
Birth : 4 April 1873 in Sherbrooke,Sherbrooke
Baptism : 11 January 1874 in Wesleyan Methodist,Sherbrooke

Connolly, Edward Worthington
Gender: Male
Birth : 4 October 1874 in Sherbrooke,Sherbrooke
Baptism : 16 November 1874 in Wesleyan Methodist,Sherbrooke