How to install WinDbg when VS 2015 is already installed?
I just ran into this same problem (with a slightly newer version of the SDK) when setting up a VM with Windows 10 and Visual Studio 2015. Following the general rule (or at least, what used to be the general rule), I installed Visual Studio first before attempting to install the SDK.
Even though I picked all the options in the Visual Studio install, and I appear to have gotten large portions of the SDK, I didn't get the debugging tools or the application verifier, which I wanted. The "Debuggers" folder was empty. Yet when I tried to download and install the standalone Windows 10 SDK, I got the error message you quote, that I needed to uninstall the SDK before I can install the latest version.
Microsoft's site is absolutely no help. It gives no clues about the appropriate way to install the software. Harry Johnston's comment got me going in the right direction.
After installing Visual Studio 2015, you already have the Windows 10 SDK. You do not need to download it separately. To get the additional tools on Windows 10:
Open Settings → System → "Apps and features".
Scroll down to "Windows Software Development Kit".
(I had two versions of it installed. The top one was newer. I'd recommend that you proceed with the newer version for the following steps.)
Select it, and click "Modify". Then, because it's Windows 10 and everything is harder than it needs to be, click "Modify" again.
The installer will launch. Select the "Change" option, and click "Next".
Place a check next to the additional features/tools you want, click "Change" to start the process.
After waiting some time, it will have downloaded and installed the additional portions of the SDK. You should now be good to go!
(This does seem like a bug in my case. The two versions of the SDK (the one I have installed and the one whose installer I downloaded) are identical (both are for version 10.0.10586.212), so running the standalone installer should just launch the same setup tool that you are able to launch from Settings, enabling me to Change/Remove Features. Oh well, at least this works.)