I now have proof that Florence Kilborn did actually exist. I have located the grave of Florence Kilborn. She is buried in Bellevue, Iowa at the Bellevue Presbyterian Cemetery*, Plot: W-4, Block 12, Old Section. The data reads: (b. around 1856 d. April 18, 1867).
First off, this fits as to why Florence was not in the 1850 and 1880 census. Most likely the date and year of death is accurate; they generally are more accurate than the birth date, especially when the birth date is stated as "around" 1856. There still is a problem with the dates or the age that she supposedly died at. If Florence died when she was 14, she would have been born in 1854. This fits with being born by the time that the town (Florence, Nebraska) was named. If the cemetery records are correct (b. around 1856), then Florence would only be 12, and would be born after the town of Florence was named. Clearly, the "around" 1856 date is wrong. Thus far, there still is no explanation as to why the rest of the family was not listed in the 1860 census.
Florence's older brother James Mitchell Kilborn* is also buried in Bellevue, Iowa at the Bellevue Presbyterian Cemetery*, Plot: W-6, Block 12, Old Section (b. May. 25, 1852 d. Nov., 1896).
If we can trust the church's records this time, Florence's brother James would have been 44 at the time of his death. Assuming that the other children lived to be older, and that Nathaniel and Hannah are not listed as being buried in or near Bellevue, Iowa, there is the possibility that they moved from Bellevue sometime after the 1880 census (the last one they are listed in). The Potter Mill web site implies that the Kilborns sold the mill in 1881, however, a book about the people of Bellevue, Iowa published in 1899 states that "Jackson Mill" is being run by James Mitchell Kilborn. If Jackson Mill is the same as Potter's Mill, then possibly James Mitchell Kilborn was running the mill after purchasing the mill from his father, who passed away prior to 1882 (possibly 1881). The same publication states that James' (Florence's) mother Hannah was living in Douglas County, Nebraska in 1899.
Hannah's mother Eliza lived until November 1881 (lived in Saratoga, an area near Florence, today part of Miller Park area), so Hannah and Nathaniel might have moved to the Florence or Saratoga area (Nebraska) to be near her, however, Nathaniel died around this time as well, possibly before Eliza, so maybe Hannah moved to be near her mother for her final days.
It is also known that Nathaniel and Hannah's daughter (also named Hannah) lived in Minnesota but later moved back to Iowa (after 1910). It is conceivable that at some point, Hannah and Nathaniel might have visited their daughter Hannah in Minnesota before or after Hannah (Forence's mother) possibly lived in Douglas County Nebraska. That too may be the final resting place for either or both parents.
Regardless of where Nathaniel and Hannah ended up, no census data after 1880 lists them. There are others named Nathaniel Kilborn but none fit the age data to indicate that they are the same as Florence's father. The others named Nathaniel Kilborn also do not seem to match up being Nathaniel and Hannah's youngest son that was named Nathaniel.
It would seem that the story ends there, but I soon found there was even more. Nathaniel and Hannah's daughter (also named Hannah) carried the family line on.
Little Florence was obviously loved by her family. Florence's sister (Hannah) and her brother (James Mitchell Kilborn) both named a daughter after their deceased sister (Florence). Hannah's daughter Florence married Thomas Edward Healey and their Florence daughter was actually Florence Caroline Healey. She grew up and married Edward Adam Kamp. They had a daughter named Geraldine Kamp. Geraldine grew up and married Charles Wesley Erwin. They had a son named Thomas Edwin Erwin. Thomas married a nice lady named Lois.
Why all the family tree? Well, it turns out that Lois is a bit of a history buff herself and she is the one that this last bit of genealogy information came from. She has traced her husband Thomas' family roots back to the 1600s. Who we know as Eliza Mitchell was Thomas Kamp's great-great grandmother.
It is from Lois' research that we know that Florence's sister Hannah moved to St. Paul, Minnesota in 1895. The Hannah that moved to Minnesota also had a daughter named Hannah (Hannah Kilborn-Healey), who moved back to Iowa later on.
Needless to say that the story is (still) not over so stay tuned.