"I have a green flag,, and she has a green flag too."
Translation:Mi havas verdan flagon, kaj ankaŭ ŝi havas verdan flagon.
It emphasises the thing it comes in front of.
So "Ankaŭ ŝi havas verdan flagon" would mean "not only do I have a green flag, but she does too".
"Ŝi ankaŭ havas verdan flagon" could mean "She not only likes green flags, she has one, too". (Though I would also use it as a general sentence, even for the "not just I do but she does as well" case.)
"Ŝi havas ankaŭ verdan flagon" could mean "She has not only a blue flag but a green one as well", or "She has not only a car but also a green flag".