Install Skype for Business via Group Policy

This will not be doable from GPO application push.  You will need to script it and have it run at logon or startup.

You need to download ODT https://www.microsoft.com/en-us/download/details.aspx?id=49117 and install.  It will create a folder with Setup.exe and a Configuration.xml as a guide for you.

Next you will need to configure a new XML file for your SFB (Your licensing model is importing here.  Are your SFB or SFB basic).  Here is a link that will help you build the proper xml config file. Here is a link to a tool that will help you build the xml file  http://officedev.github.io/Office-IT-Pro-Deployment-Scripts/XmlEditor.html.  I have not used the Install Tool feature, but it looks like it will package up an MSI for you and will make it possible to push out via GPO, but if you are going down the standard route you will need the config file.

Once the config xml file is create you will need to add one extra element for the path to store the download.

The   <Product ID="SkypeforBusinessRetail"> is very important that you have the correct one you are licensed for.
https://support.microsoft.com/en-us/help/2842297/product-ids-that-are-supported-by-the-office-deployment-tool-for-click

<Configuration>
    <Add  SourcePath="\\Server\Share" OfficeClientEdition="32" Channel="Broad" ForceUpgrade="TRUE">
        <Product ID="SkypeforBusinessRetail">
            <Language ID="en-us" />
        </Product>
    </Add>
    <Display Level="Full" AcceptEULA="FALSE" />
    <Updates Enabled="FALSE" />
    <Property Name="FORCEAPPSHUTDOWN" Value="TRUE" />
    <Property Name="SharedComputerLicensing" Value="0" />
    <Property Name="PinIconsToTaskbar" Value="TRUE" />
</Configuration>

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Once these steps are down you will now need to run Setup.exe /download  "NewConfig.xml"
https://docs.microsoft.com/en-us/deployoffice/deploy-office-365-proplus-from-a-local-source

\\server\share\O365\setup.exe /download \\server\share\O365\config-group1-SAC.xml

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Once the download is completed you will then need to create a Startup or Logon script that looks like this

\\Server\Share\O365\setup.exe /configure \\Server\Share\O365\config-group1-SAC.xml

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Hope this helps

Thanks.  I'm trying this now.  Will let you know how if it works.

It's a bit a process at first, but you will get the hang of it.  
I wish the MS just made a MSI for people that have Office 365 in enterprise environment, but they do not :(

How do I make the .cmd script for group policy?  This tool does all but that.

So the downloaded part is done and the next step is to create the CMD file with the proper syntax:

\\server\share\O365\setup.exe /download \\server\share\O365\config-group1-SAC.xml

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Now you will need to a similar command and paste in a .bat or .cmd file.

\\Server\Share\O365\setup.exe /configure \\Server\Share\O365\config-group1-SAC.xml

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Add the startup script to the GPO that points to the BAT or CMD file.

This is the best way I know how to accomplish without some sort of application push.  

does that make sense?

For some reason, doing it as a Startup GPO isn't working.  I tried both Software Installation and did it a Startup Script.  But, when I move the .cmd to a Logon Script, it works but, it asks the user for admin creds to allow the install.  If I were to keep it as a Logon Script, is there a way to force the install with admin rights so the user doesn't need to type anything in or call me to put the creds in for them?

Software Installation will never work with exe.
You can added Logging to the XML file to see where it failing.
https://docs.microsoft.com/en-us/deployoffice/configuration-options-for-the-office-2016-deployment-tool#logging-element

<Logging Level="Standard" 
         Path="%temp%" />

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What if you manually run your bat or cmd file?

I'm not using an exe.  I'm using a msi created from the link you sent me yesterday.  I'll implement the logging command to the xml to see what I get.

I always like to test scripts manually for validation.

Could it be that I put the .msi's channel as Monthly instead of Broad?

that does not affect the deployment.  That option is how often it does feature updates.  I most cases enterprise deployments do not like to be updates to the newest versions so quick because add-in and things like this may not work.  

So <Broad> just means every 6 months the version is updated

You may have a failure somewhere else (e.g. Security access to the files or an incorrect UNC path).

Okay thanks.  Still trying to figure this out.