How do I subtract one selection from another in PS CC?

Mike I hate to make this over complicated, as I suspect I would load the luminosity mask selection, turn on Quick Mask, Ctrl click the sky alpha channel and use Alt Backspace to fill with black or white (depending on how you like to have Quick Mask set)

So to go back a step, you have run the Luminosity Mask ( I am using Sven Stork's Interactive LM)

Drag any channel to the new channel icon to save it as an alpha channel

Select the sky, and save it from the Select menu

Then do what I said with Quick mask.

But if things were complicated, then you could use Calculations.

Create the two alpha channels as above.

Select the LM alpha channel and run Image > Calculations

Source 1 will default to the LM Channel you had selected

Use the drop down in source 2 and select your Sky channel

Set the blend mode to Multiply, or Darken.  Even Merged will work in this case.  Note that you have an option to Invert source 2 — you obviously need the sky to be black.

OK that.

Now click on the RGB channel to get your picture back and Ctrl click the new Alpha Channel to load the Luminosity mask minus the sky

I have turned on Quick mask to make it clearer, but...

...it might work better if you copy the background layer

Ctrl click the new Alpha Channel

And add a layer mask

Like I said above, it feels like a sledge hammer to crack nuts in your case, but it's a useful tool to have.

It's used a lot with difficult selections by working the red, green and blue channels against each other.