When a girl flirts with me, does that mean she's eligible for marriage?

Occasionally, while wandering around various cities, some female NPCs seem prone to flirt with me. They'll say things like "It's a fine day with you around" and such.

Is this an indication that they can be married?

No. That just means you've improved their disposition towards you by doing a quest to help them. Male NPCs have equivalent dialog as well.

in order for marriage to be elligible you must have the amulet of mara equipped. You can purchase one from Maramal in riften for 200 septims. while wearing it eligible NPCs will comment on it when you initiate dialogue with them. If you would prefer a list of eligible NPCs without searching it can be found here:

http://elderscrolls.wikia.com/wiki/Marriage#Potential_spouses

Hope this helps!