The only thing Brown/Shattenkirk would do is save them $3m. While saving $3m is nothing to sneeze at, at this point, do you really think they would trade him, only to force him into free agency in late July/August? He'd have to find another team, move the family, etc. The time to get rid of him would've been years ago. Now, with everything that's happened to the franchise, there's no reason to do that to him. He's firmly entrenched in LA, personally and professionally. Again, $3m would be good savings, but unless he asks to be traded, he is very likely to retire as a King(save a ridiculous trade offer). He will be very content doing so, and I imagine the organizational will be very content in seeing it happen.
The Brooks would throw his name out there makes Brooks an idiot. He clearly has no concept of what the Kings are doing.