The engine on my 2006 road king shuts off when down shifting to lower speeds

SOURCE: shift pattern

1st gear all the way down (toe shifter, not heel). Lift up N,2nd,3rd,4th,5th-6th(if applicable)

SOURCE: 2001 H-D Road King engine knock

01road king..probably have 30 to 40 thousand on it...Sounds like cam chain tensioner..about the only thing that will go wrong with your bike. I will assume you have oil etc in it...If you have not been running your bike stupid then nothing mechanical will usually brake on a Harley. Once again I assume its stock. You don't have an oil light on so I'll put my money on cam chain tensioner has exploded or is about to.

SOURCE: Oil change directions, 2003 Road King

The drain plug is on the left side of the oil reservoir pointing towards the front of the bike. The motor should be warm when you dump the oil and the o-ring should be replaced as an extra precaution (don't want to waste that new oil if you have a drip). When replacing the oil filter use a piece of tin foil to divert the oil to your waste pan.

SOURCE: valve noise 2006 road king

Hello redevil67...This is normal for the HD engine, it going to have valve train, top end noise at some point, some as early as 2000 miles. If you take it to the dealer they will try to sell you on worn tappets...key word here SELL..I've seen this many times, dealer replaces componets, 2000 miles later the noise returns.
These are hydraulic valves and as you probably know they operate at zero lash. Personaly, i feel that the problem is that the cams are not hardened properly or machined incorrectly.. When the leading edge of the cam lobes wear to a strange profile it tends to snap the lifter up in the lifter bore. This causes the rest of the valve train to rattle. You hear the noise on top but the culprit makin it, is the cams..Many chose to go with an aftermarket cam, such as an andrews...Another suggestion, is to switch oils. Don't know what you are useing now, but i'm not a fan of dino oil. As the temperature builds the more an oil is stressed. Lucas full synthetic 20w-50 or Mobil1 15w-50 are both excellent for anti-wear and long term protection.
I hope this helps, please rate me a fixya and good luck with your bike.

SOURCE: link for down loading harley davidson road king repair manual

Not going to happen, copyright issues just like music. You may find it but.......