It should be perfectly fine. Most manufacturers have their own little plastic piece that fits in the back panel. Switch out the plastic piece and the slides go right in. Quite possible that King has the same extrusion shape and could be very simple. Most manufacturers try to make things interchangeable as much as possible.

Mounting the fronts are simply to the face frame, so no issues there.

I remember your problem. Frameless cabinets, yes?
With your issue could be any of a few things going on. Blums will definitely be an improvement
Possible the original holes became stripped. If the kiing and blumm have same hole pattern then use the old holes to mount the new glide BUT then drill new ones using. 5mm "Vix" bit and use euro screws.
Check the fit of the glide to the box. There is a notch and a hole at the back. It is not the same for all makes. But King is a pretty close knock off. Besides sounds like there is a good chance your boxes were made for blums and not king whcih could be the root.
Lastly check the thickness of the drawer box sides, will be either 3/4 or 5/8. . Look up blum glides, find the one made for your thickness and write down the number. That should be stamped on the glide.

jakuvall - sounds like you have done this before! We will have our kitchen installer change out the glides but at least I have an idea of what is going on. Why euro screws ( what are euro screws lol)

The only other thing I wonder is if I actually have the other brand that they manufacture in the same plant.

I noticed when I took this photo that the side of the drawer has the name of the cabs stamped on it. It's possible your cabinets also have markings. I honestly never noticed this until I was looking at the photo.

Have built, fixed, , repurposed, changed and otherwise mutilated a lot of things over the years :)
Euro Screws have a wider body and wider space between threads. They tend to work better in engineered materials AND the heads fit perfectly in blum glides.

Here is a link that might be useful: Euro Screws

Suzanne - the odd thing about my drawers is that none of the drawers in the island or the main kitchen have Cabico stamped on them. I also had two other Cabico units installed. One was a command centre type area with drawers, filing cabinet and upper cabinets. The drawers in this unit have the Cabico stamp. This unit was delivered at the same time as the main kitchen cabinets and island. About 6 weeks later I ordered another ten feet of base cabinets with drawers. All the drawers in this unit are stamped. So only some of the drawers are stamped and the stamped/ unstamped drawers are consistent within the particular unit....ie: there is not a mixture of stamped and unstamped within the island or the main kitchen cabinets.

I have asked a couple of times why this is so, but so far no response.

One of the early theories on my glide problem was that the screw was stripped. How do you know when to stop tightening the screw?

Hand tighten, snug is enough. Only way to describe it. Also if you do use euro screws they are usually "posi-drive" they look like Phillips head but are not. Your door hinges will also be posi drive. It's a good idea to get yourself a posidrive screwdriver (I prefer the Hafele but Blum also offer one) cabinetparts dot com or the like.
I give them out to installers all the time so they don't strip screws when adjusting doors.

Way to stick with it! Can't wait til your problem is resolved. I expect my problems (not the same) to be resolved within the week!

Hi muscokasrp! Just wondering if your issues were resolved. Also wondering if you live in the muscoka area and if you would recommend your kd? I live in TO but have a cottage in Gravenhurst. Thanks