Brinley is NMS, but I prefer that spelling to Brynlie (Brinley looks like a family name, Brynlie looks made up).
Why not just name her Brynn, if that's what you are going to call her?
I think Brynn is a better match with Brady. Brinley and Brady is a little cutsie.
I do not like Brinley with Avery, or any other name that has the same ending.
Addison Avery and Peyton Avery are very androgynous names, though they flow nicely. I would choose something more feminine for a middle if going with a surname first name.
Also, I feel like Addison and Peyton are becoming very popular, so that would be a concern for me.