1997 road king acts like its dying,pops and misses sounds like carb is sucking air

got to have fuel, spark, air and compression. your missing one. be sure plug is good. give it a shot of carburetor cleaner. if it starts and dies it is fuel. check compression. take off valve cover and be sure valves are working as they should and gaped correctly.

Sounds like the carbs are dirty, The mail inlet where the float works to shut off fuel when the bowls get full has a screen just under the needle valve and there are stopped up with crud, Pull the bottoms off and remove the float & needle valve and the the seat and clean, If you see dirt inside the float bowl then remove the jets and clean them also.

Backfiring out of the exhaust is usually an ignition problem. Unburned fuel is getting into the exhaust system because it's not being ignited in the cylinder. When the engine fires on that cylinder again, it ignites the raw fuel in the exhaust causing the pop that people call a backfire. I'd investigate the ignition system. Connect a timing light to each of the spark plug wires if it has a single fire ignition or either of them if the ignition system is the stock dual fire. Start the engine and watch the timing light to tell if the engine is missing as the light will miss a flash.

Good Luck
Steve

The timing chain most likely adjusts itself( I am not certain) however a loose chain will cause an engine rattle, but is not the cause of popping and dying.
try cleaning the fuel system, new spark plugs,new air cleaner

Check to see if you have a good fuel supply to the carbs ,and that none of the air / fuel jets are blocked .

well check all fuse first then check wires to coile and see if you have volts on one of the wires it should be at least 12 volts the on the right side of bike right about were foot floor board is that round cap buy the foot is where ignition module is there should be little wire harness coming out of there that harness runs long frame may have Ben hit damaged wire in it look under floor broad and foll the wire to see if damaged hope this helps

have had a few of these in with carb faults but were 2 barrel type.basic checks first,is pcv valve hose under carb not split(runs to valve cover or oil cap on this model?).try driving without airfilter element for test,have had one in that looked clean but had a fine mist of oil on it that blocked and caused air starve and stall on power.Did both problems start at same time? or maybe you are chasing 2 probs.being a ute.I have had probs with rusting petrol tanks and blocked fuel filters

If you have carb, it may need to be adjusted,
Or fuel injectors if you have them.
Could be plugged blow-valve
Valves may need to be adjusted

do not think vacuum hose is teh issue. When ws last time you replaced fuel and air filter? Couls also be failing fuel pump, so need to check output pressure. If check engine light comes on may be in air polution control system. Need to pull code and see what circuit is causing the fault code. Sometimes an auto zone will read code for free.

Sounds like the intake manifold is leaking. The area where the leak usually happens, are those two rubber sleeves that go from the heads, (Cylinder heads) to the intake. Sometimes the clamp/s loosen up. Sometimes these rubber sleeves deteriorate, and cracks form.

This makes the engine backfire, pop, and idle fast.

The added air at the wrong time cause a backfire, when you let off the throttle. The added air causes the engine to pop, because the exhaust valve has sucked up some cold air.
The engine idles fast, because more air is being introduced, and not metered by the injection system.

(The exhaust valve thing. Exhaust valves are supposed to open, and let exhaust out right? Well there is a thing called Valve Overlap.
The Exhaust valve hasn't closed all the way yet, and the Intake valve is opening.
The 4 stroke engine, (Of which a Harley is), has these four strokes.
1.Intake Stroke. Fuel/air is sucked in.
2.Compression Stroke. The piston comes up and squeezes the fuel/air mixture.
3.Combustion Stroke. The spark plug lights the fuel/air mixture off.
4.Exhaust Stroke. The spent gases are expelled out.

Your Road King has one camshaft. There are four cam lobes on it.
Intake, Exhaust, Intake, Exhaust.

If you had the camshaft in your hand, and had the gear end facing you, look down the camshaft. You will see those egg shaped cam lobes. You will notice that No.1 cylinder Intake lobe is facing to the left.
No.1 Exhaust is facing to the right.

If you put a degree wheel on the gear end of the camshaft, and had the No.1 Exhaust lobe ramp nose facing straight up, you would see that it's about 110 degrees, before the Intake lobe ramp at .050 lift, comes into play. (The roller, of your roller lifter has raised the Exhaust valve up .050 inch) There is about 55 degrees before the Exhaust valve hasn't quite shut.
This is okay for normal running. Introduce a vacuum leak, and the surge of extra cold air, makes it pop.

Solution? I suggest checking to see if the clamps on those rubber sleeves are loose. You can also spray WD-40 towards the ends of each rubber sleeve, when the engine is idling, and see if it speeds up. Means, one or more, of those rubber sleeves has deteriorated.