I have an application compiled in VS 2015 and requires the VC++ Redistributable package in order to run properly. Prior to this latest build, we were using an older version
I found this question and tried it myself, being in the same situation. I found the installer error you're running into was/is Error 1618: "Another installation is already in progress." It seems that running the vc_redist installer inside your own installer simply won't work.
Your other options seem to be creating a bootstrapper as Patrick Allwood suggests above, or simply asking users to install the vc_redist package on their own before running your own installer. You can detect if the Universal C Runtime is already present by checking for ucrtbase.dll in C:\Windows\System32:
If you only have a 32-bit installer, you can also use the [SystemFolder] property directly.
EDIT: As Kevin Smyth mentioned, the version of ucrtbase.dll is giving weird issues - reporting version 2.X to some tools, and version 10.Y to other tools. You can remove the MinVersion property if you just want to check for the existence of ucrtbase.dll.