I would say [name_f]Briley[/name_f] / [name_f]Brilee[/name_f] / etc is usually bry-lee, in the style of [name_f]Riley[/name_f], [name_f]Miley[/name_f], etc. I’ve only heard it said that way and would definitely assume ‘bry’.
[name_f][/name_f]I would probably spell it Breeley, Breelee, or Breely to make your desired pronunciation clearer.