You should be able to ask Sir Patrick about the breastplate, and he will have a quest for you in order to get it. During the conversation, if you claim it just an old, rusty breastplate to try to keep him from realizing its value, and eventually use the dialog option "Er... Lets forget about it...", Sir Patrick will indeed forget about it, and you will no longer have to option to speak to him about it.
If it didn't come up in the first place, try going back and talking to the dwarven king and the smith Grisha again, and return to Sir Patrick. A couple people have had problems getting this quest from Patrick, but usually just talking to everyone again a couple times is enough to trigger the proper dialog with Patrick.
