The only Mary to marry a Flynn in Maryland at the right time is a woman named Mary Ann Richardson. All other Marys who married a Flynn in Maryland in the correct time period can be shown to not be the Mary who was the mother of Mary Edith Flynn. According to 1880 census both of her parents were born in Maryland. However according to her death record her dad was born in England.
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MX6M-RZL : 12 April 2016), Mary Flynn in household of Simon Flynn, Washington, ward 2, Washington, District of Columbia, United States; citing family 1126, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"Maryland Marriages, 1666-1970," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F4JX-18H : 12 December 2014), Simon Flynn and Mary Ann Richardson, 09 Sep 1843; citing , Baltimore, Maryland, reference ; FHL microfilm 13,694.
Find A Grave Memorial# 176886109
"District of Columbia Deaths, 1874-1961," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:F7BM-N5T : accessed 14 September 2017), Mary Flynn, 26 Oct 1896, District of Columbia, United States; citing reference ID 3162, District Records Center, Washington D.C.; FHL microfilm 2,115,023.
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R > Richardson | F > Flynn > Mary Ann (Richardson) Flynn