Hello. I have a client that wants to display articles from the main site/domain on to a subdomain site. Each site has it's own Joomla install, but I believe they share the same database. Is that possible with this tool?

To share the article, you need the JMS Article Sharing that works with JMS.
/index.php?=0&cartReset=N&redirected=1&option=com_virtuemart&Itemid=1
And see the video that explain the concept and how it works
tutorial.jms2win.com/joomla/multisite-12...ingforjms/index.html

This extension require JMS to work.
In fact, the Article Sharing READs and connect the remote website to read the articles with their content.
The connection on the remote website is done via JMS that has the code to connect on any website. The connection is based on the JMS "Site ID".

In your specific case, as you have independent standalone webisite to be able reading the other website, you should install JMS on a website and declare the other slave site.
When done, as you will have one "master" and one "slave", you will be able to read the article from the other site.
The tips is to create a "fresh" slave site that point the directory of the existing standalone website.
So that the JMS Site ID will be defined and could be used by the Article Sharing for the connection to read the article present on the other website .

In summary, this is possible and you need both JMS (ie basic) + the "Article Sharing for JMS".

Can I have multiple Slaves?

YES.
In the case where you are using "standalone" website, you will have to install JMS on each sites where you want to install the Article Sharing.

I have JMS and Article sharing installed on my Master site. I am unable to see the articles on the save site. I have not found the documentation to be very helpful as to why. Do I need to install an extension on the slave site?

Normally, you have to install JMS only on the master website because the PHP Code is shared between all the websites and therefore is available for all internally.

In your specific case, you mentionned that you are using independent standalone website. Therefore, you need to install JMS on the slave site to allow the JMS application (PHP code) available in the slave site. In this case, to allow the Article Sharing call the JMS internal code.

To see the other websites, you need to declare them in JMS.
The key element is to have the correct "deploy folder" that correspond to the place where the other site are installed and where the "configuration.php" is located.
So you have to install JMS in each standalone webssite where you want to install the Article Sharing. Once JMS is installed, you have to define with the JMS Manager the other website on which you want the Article Sharing is able to connect.