You should not get that warning at all if your account does not own the game but your brothers.
Are you sure you are on the right account/did not buy it for your own account instead of your brothers?

Each account can only own one copy of the game. You can't somehow own two because you're in a family group so that two of you can play. If another person wants to play, someone else in the group will have to own a copy.

If you are getting that message, it means whatever you have placed in your cart is something you already own. You can still gift it to someone else, granted they also do not own it, but you won't gain an additional copy.

You can not family share games that require a 3rd party account to play, bf6 falls under this.

To simplify how steam families game sharing works here is an example:

1. Brother owns a gamed called ABC (this game meets all the requirement for family sharing).
2. Sister has no games on her account.

A. The sister can play her brothers game ABC through the steam families. But only if the brother is not playing it.
B. If the brother is already playing ABC, the sister will have to wait for him to finish before she can play it.
C. If they both wanted the play the game together then the sister would have to buy her own copy on her own account.

A third person joins the family group, lets say for example a cousin and they also own game ABC.

The sister could play her brothers copy of ABC together with the cousin who is playing their own copy of the game. Only 2 people can play the game as the group only has 2 copies.
Again if all 3 people wanted to play together, the sister would have to buy her own copy of the game.