Well, the name was originated within the Court, it was nickname given to it by French nobles over the years. So, I don't really think I've helped you much there!
The name in itself means that it was a squadron with very relaxed moral attitudes! It played with the sense of the verb to fly, meaning that the women that integrated the group were 'of easy virtue'. I don't think I can explain this better as I think there's no equivalent with a similar meaning in English.
But for those who speak French the thing would be: to fly; birds fly; birds are supposedly of small weighth (léger). The word 'léger' can also mean that someone is frivolous and of easy virtue. So there is the meaning.