Petemac,
This appears to be a common thing with the kings. There are many threads here about this.
I have a 2000 RK that had the same problem. There are a couple of fixes from what I read.
I replaced the brakes with the kevlar Lyndall (sp)Racing brakes. I think there is a rep on this site. Also got some brake cleaner, about 4 cans, and cleaned the pistons at the same time, and it worked for me. If you go to Lyndall Racing web site there is a procedure spelled out on how to replace. Like others say if you don't feel comfortable doing it, don't, its the brakes we are talking about, but it is pretty simple.
The other option is to switch the two front rotors from side to side, and people say that fixed the problem as well.
Do a search on front brake squeak, or something simluarand you should find some info on it,

 

Yep....Normal all the way back to 1994.It is actually the nature of all disc brake systems just seems to be more pronounced on Road Kings for some reason.

 

Thanks again for the replies. I think this is a partially frozen caliper piston. I've had the bike over 8k miles and I just started hearing this. What's odd is that before the only thing I heard from the front brakeswas the"swishing" sound when the front brake is applied like glebo mentioned. But here's why I think there's a problem.....now I hear the pads on the rotors as I'm moving the bike slowly and now when I apply the front brake the sound goes away instead of the old swishing sound! Does this sounds like a stuck caliper piston?

 

Petemac,
That is the same exact problem I had. Heard a noise at low speeds, and when I applied a little pressure top the brake lever it went away. It almost sounded like the rotors were warped. Cleaned the pistons and replaced the pads with the Lyndalls and it went away.