Need Help with Multiple Placemarks Map

Sorry. I didn't understand you.
You have a few maps, and 3 placemarks.
You call plugin to show this 3 placemarks on definite map?
Or you just want to show map with its map objects.

If you want to show only definite placemarks on map - call plugin by placemark list and enter its IDs
If you want to show map with its placemarks - show by map call, you don't need to enter all IDs. Just the other call clause.

Plugin call by placemark list, group list, category list - it is way to show map from different maps or by some restriction.

I have 1 map. 3 placemarks. On the locations page I have added the code: {zhgooglemap-markerlist:1,2,3;1;15} . I was expecting to see all three placemarks for the 3 locations.

As I stated previously, I was using a different google maps plugin that is no longer being managed and had a kml file that provided the 3 locations previously. I would prefer to use a KML file as I have this same format for many sites. I haven't been able to figure out the details for the kml file as the instructions are just not clear enough. This is my preferred method for multiple location maps.

If the kml file is not going to work I just need to see how to show multiple locations on a map. There are many options and I've been trying them all with partial success.

You state specific things to do but I still am not getting the syntax correct. In the documentation you point out specific rules, but ultimately the examples were more helpful than the details after the fact.

Based on this further detail, can you recommend the best way and an example of the correct syntax

You can display map by menu item (Map), by module and by plugin.

Plugin common use - display map in an article.
There are different cases to show map by plugin.
If you have one map with 3 placemarks, just call {zhgooglemap:1}
This call show map with id=1 and show all published map objects (placemarks, paths, routes and so on)
KML file you can show by 2 way
1 - enter full URL (with http:) to file into map details - you just show it without addition options.
2 - create path and enter into KML section full URL to kml-file, and you can set addition option (change zoom to show all file data and enable/disable infowin for this file

As for KML vs Placemarks
As I can see on your contact page - if you create placemarks for your Affiliations - you can not only show it on map, but also enter any contact data into infowin content, but also create your placemark list automatically. For example by predefined positions or in external position (where you want).
But one notice - if you enter email into infowin content, you have to disable joomla email cloaking plugin or enter this email by code, which that email plugin will not process. Because it will broke my code.
Or you need to enable ajax loading infowin content or all placemarks - in this case email cloaking plugin doesn't process data.
By method #2 you can show not only one KML file on map

As for placemarks
In page body I can see placemark creation
But I can't access to images of icons
I can see path to it "www.collprofinc.com/components/com_zhgooglemap/assets/icons/"
It means you enable compatibility mode for resource files
But you can read more correctly my documentation - for resource files - you have to copy icons from admin folder to site.
I notice about that in documentation - because there are a lot of icons and I don't want to produce double size archive for this case.