Hi Debby,
Thanks for the details on Ellis Island, I did not know all that about the year it opened etc.
Here are some details that might help out of you can find Marys marriage certificate:
The parents names of (my) Flynns (i.e. the parents of James and Michael who emigrated to USA) were:
James Flynn
Anne Flynn (formerly Keaveney, also have seen it spelled Keaveny or also Caveney on a marriage Cert of Sarah E Flynn in Springfield, MA).
They were from the Catholic Parish of Templeboy and Kilmacshalgen, Co. Sligo

Other siblings names I have, including Mary, are Hugh Flynn, Bridget Flynn(died aged 13), Patrick Flynn(believed to have died as a child), John Flynn(emigrated to England), Sarah Ellen (emigrated to Springfield, MA, married a man named Michael Tuohey), Margaret-Anne (married a man named Andrew Kilgallen and lived to be 96 years old in Sligo) and Thomas Flynn(my grandfather, who stayed on the farm and in the homeplace.
As I mentioned before, there was a Mary Flynn born to James and Anne Keaveney but we did not know what happened to her. My father (now deceased) never met or heard anything about Mary or James or Michael Flynn (the latter 2 who we understand from relatives emigrated to USA) and he said they never wrote to hs father or returned to Ireland. This may or may not be true as my grandfather Thomas was the youngest of the 13 children (8 of 13 that I know of survived) and my own father was also the youngest of his own family.
I have two Flynn aunts still living who are in their eighties but they do not recall Mary either and my fathers first cousin who is 92 years old with an excellent memory helped out with some of the details above. Any new facts you find about Mary may help jog their memories. All of them have excellent memories still.

Do you have a date of birth for Mary or where she live initially when he went to USA?

Hope we can find out more and maybe make a connection

Kathleen