it depends on how you're going to build it up, as a rifle or an SBR. I'm going to assume SBR since you mentioned paperwork.
This is just my understanding, but I would recommend you call around to several smiths that you would like to build your rifle 1st.
You can ship directly to the builder and they can ship directly back to you. They will require a copy of your Form 1. The issue here is that it's at your brothers house. If he is out of state, the proper thing to do would be to have it transferred back to you. Now, I have been able to legally send myself my own rifles out of state for a class, and then send them back to myself without using an FFL. I'm not sure about the legality of your brother sending then kit to smith for you, and then having it sent back to you as a built weapon.