Five years before the beginning of the game, Sir Fratley promised Freya that he would return. He left their home, Burmecia, in order to keep peace. (According to a game quote, he planned on travelling around the whole world before returning to Burmecia.)
After two years, Freya also left Burmecia in order to search for him since he hadn't returned. (This prompted Puck, the prince of Burmecia, to leave one month later). She heard rumors about the places that Fratley travelled, along with other rumors that he died. Later, she settled in Lindblum, where the gamer would eventually meet her.
Since these events took place 5 years prior to the beginning of the game, that would put Freya at age 16 when Fratley left, and 18 when she went to search for him. It isn't specified how old she was when she met Zidane. It also isn't specified at what point she became a dragon knight, but it's safe to presume that it was at least by age 18, since it isn't mentioned that she returned to Burmecia before journeying there with Zidane.