Your sentence
There were two girls, either with a flower
sounds awkward, I think you probably mean
There were two girls, either one had a flower
"Either one" means both people and since you are saying they have flowers with them, the possessive "had" is used.
Only using "either with a flower" leaves the reader suspended since they would be waiting for something like
either with a flower or with a ribbon
Using "either one" would mean both have flowers and there would be two flowers.
There were two girls, neither had a flower
is understandable since you are using the possessive "had" meaning there were no flowers. If you had used
There were two girls, neither with a flower
a similar ambiguity would occur
neither with a flower nor with something else
would be expected.