Embedding a SimpleViewer gallery in a WordPress page is essentially the same as embedding a SimpleViewer gallery in any other HTML or PHP page.
I would recommend using the baseURL method of embedding, i.e. uploading complete gallery folders (not just their contents) and following the instructions here.

You can certainly have multiple galleries on the same page but SimpleViewer does not provide functionality whereby a 'cover/image to represent each gallery' can be clicked for the gallery to spring to life. Also, there is no built-in Lightbox functionality.

If you just wanted to have two galleries on the same page, the following example would work.
Say you have two gallery folders named 'gallery1' and 'gallery2' and you uploaded both folders to the root of your web domain (in this example named 'www.example.com'). The embedding code you would use would look like this:

<script type="text/javascript" src="http://www.example.com/gallery1/svcore/js/simpleviewer.js"></script>

<script type="text/javascript">
var flashvars1 = {};
flashvars1.baseURL = "http://www.example.com/gallery1/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container1", "100%", "100%", "222222", true, flashvars1);
});
</script>
<div id="sv-container1"></div>

<script type="text/javascript">
var flashvars2 = {};
flashvars2.baseURL = "http://www.example.com/gallery2/";
simpleviewer.ready(function () {
simpleviewer.load("sv-container2", "100%", "100%", "222222", true, flashvars2);
});
</script>
<div id="sv-container2"></div>

The things to note are:
(1) You need only load one instance of 'simpleviewer.js' per page.
(2) Each gallery must have a unique 'flashvars' variable name.
(3) Each gallery must be embedded into a <div> with a unique name.

If you wanted to use a placeholder for each gallery and open each gallery in a lightbox, a suitable lightbox script capable of displaying a SimpleViewer gallery is Shadowbox.
You would then:
(1) Upload each gallery folder in its entirety (as above).
(2) Insert an image into your page for each gallery and link each image to the corresponding gallery's 'index.html' file using standard HTML <a> tags and the Shadowbox 'rel' attribute as documented on this page.