I just got done the process, and have a 14' aluminum flat boat that I purchased from my brother-in-law with no HIN (1969) with last registration from 2005 in Alabama (which doesn't title boats and no title or registration on trailers)

1- Get notarized BOS for boat and trailer separately, along with copy/original registration form out of state

2 - Fill out R1331 downloadable from LDWF

3 - Bring bill of sale, registration, and R1331 to State department of Revenue (Baton Rouge open everyday, New Orleans only open tues/wednesday by appointment at 1450 Poydras in the pink building across from superdome, 8th floor I think [NOT 1555 Poydras like everyone says]. Make appointment about 1.5-2 weeks in advance) R1331 must be filled out by state before going to Orleans Parish tax authority no matter what the people on the phone tell you.

4 - Bring R1331 to City Hall, Bottom Floor, make right after entering through metal detectors at
main entrance, office is the LAST door on your left. No matter what they tell you, you do not need to fill out some long crazy application form. The ladies at the application window on the far left will sign and notarize R1331.

5 - Bring completed R1331, NBOS, and ORIGINAL Registration from out of state signed by previous owner to LDWF in Baton Rouge. $23 and 10 min to 1.5 hour wait and they will hand you the stickers.

A few notes, if your boat is missing a HIN and it is pre 1972 then the processor claims you are still within the elligbility to be registered (different from the LDWF website, but confirmed by the boating regulations handbook received upon registration that is suppose to be the most current). I would make a copy of your BOS because LDWF wants to keep the original.

The trailer seems like its going to be a whole nother story. I just called the State Police and got automated message telling me in order to get the trailer inspected and a VIN stamped that I'll need:

1) affidavit/Judgment of Award from a Justice of the peace ($60 bucks from Jefferson Parish at 1803 Williams BLVD, 504 - 466-7984. The lady that picked up the phone sounded very knowlegdable and forthright, which was a pleasant surprise after dealing with all the tax BS in Orleans. She did however say its not garunteed and that the Judge has to review all paperwork ect.)
2) Title, Registration, OR Bill of Sale
3) Current Proof of Insurance

I'm assuming I have to get the inspection done before I can go over to the DMV and get the trailer registered/legal. On my way to the Justice of the peace now.

PM/email/comment if you have questions about the process I went through for Orleans/LDWF. When I was going through this I was hardpressed to find info on a out of state boat pre 1972. I'll try and post if I ever get the trailer done. I also wanted to post because I have tons of time off right now, and couldn't imagine getting this done if I was currently working. The boat issues could have been taken care of in a single day with the list I gave above if your appointment with the State Department of Revenue was early enough.