I have exhausted my own creative thinking on this matter. I found only one probably reliable record and that was the 2nd marriage of Frank Oliver Blake.
In the matter of the marriage of Frank O. Blake (age 40) to his 2nd wife, 13 Jun 1910, Windsor, Essex, Ontario, Canada, to Lizzie McIntyre (age 37), Frank's parents are listed as George Blake and his mother as Anna Flannery [Ontario Marriages, 1969-1927]
Both parents are indicated as having been born in Ireland in other material; that may be the case
THERE is a George Blake age 23 in the 1850 Census living in Danby, Rutland, Vermont; b. Ireland; whether he is married to the woman Catherine Blake isn't known, since it isn't listed
There's nothing reliable to be found, meaning I do not find a census with Frank O. in it with his parents "Anna" and "Frank" or "George" together in it, nor do I find any listing at Find A Grave that would indicate either parent was buried in Vermont
Since Frank Oliver was born in Vermont, apparently born in Vermont, and it is believed his parents were born in Ireland, they must have immigrated prior to 1870. Nor anything to indicate that one or both of Frank Oliver's parents were married at least twice.
There's nothing to confirm that Anna's maiden name was Flannery; there's nothing to confirm that Frank (George) or George (Frank) is the father other than the marriage record of Frank Oliver, which occurred in Canada.
You might have to read the entire Vermont Vital Stat offering for further clues; I suppose it IS possible Frank Oliver's parents went to Canada? Vermont and Canada are not that far apart.