At the moment, your web page uses the following code:
<script src="jbcore/juicebox.js"></script>
Therefore, the 'juicebox.js' file should be in this location on your web server: http://designcuisine.macyscatering.com/gallery/jbcore/juicebox.js
... but going directly to that location in a browser results in an error 404 (file not found).
It looks like your gallery files have not been uploaded to the correct location on your web server.
If you are trying to manually embed a gallery into a WordPress post, then I would recommend using the baseUrl method of embedding as documented here.
Essentially, you would create a Juicebox-Pro gallery on your computer with JuiceboxBuilder-Pro, upload the complete gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into the body of your WordPress post making sure that the method of entry is 'Text' rather than 'Visual'.
It does not matter where on your web server you upload your gallery folder to as long as the two paths within the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.
Alternatively, you could use the dedicated Juicebox plugin for WordPress, WP-Juicebox, which allows you to create and edit Juicebox galleries within the WordPress Dashboard. All the embedding code is automatically handled by the plugin and there is no need to worry about any manual coding.
WP-Juicebox can be downloaded from this web page. Instructions for use are on the same page.
Am I incorrect in thinking; by using my Flickr account, my images are already online so I do not need to upload them?
That is correct. If you want to source your Juicebox-Pro gallery with images from your Flickr account, then you can use set useFlickr="TRUE" and use the other Flickr configuration options (in the Lite and Flickr Pro sections) to point towards them.