Items not being recognized by other Joomla extensions

Understood. I have a menu link to the Category: group.cruiseandvacationdesk.com/cruises-21/oceania-cruises

That works correctly. It's the items being displayed in that Category view that are missing their item ID. I do not have menu links to each article...too many and they change too frequently. I was using the Tagged Category menu item type to create the menu item link and then listing all the items with the appropriate tag(s) within that Category. The links (non-sef) are being generated by Flexicontent.

Where/How do I configure Flexicontent to include that item ID?

you need to create link to each category (maybe in hidden menu)
for exemple : group.cruiseandvacationdesk.com/content_page/item/171-alaska isn't a good url, that create because you didn't have a menu link to initialize your sef rooting (iys a joomla concept)
if sef is realy initialize you url become
group.cruiseandvacationdesk.com/yourcategoryname/171-alaska

I noticed that in the FlexiContent Config Under SEO & SEF URLs that Remove IDs from URLs was set to NO, I changed to YES. Saved, then purged all SEF URLs and cleared cache and reloaded the home page and tried navigating to the landing page and am still getting the home page view for any item linked on the category page.

The new non-sef url is: group.cruiseandvacationdesk.com/index.ph...24&id=1285&view=item

The new sef url is: group.cruiseandvacationdesk.com/componen...m/1285-save-up-to-10

As i explain your sef ul are wrong
its not good for seo to display component/flexiocontent/item/id-nameofitem
you need to check your menu structure to change this for a good url structure
categoryname/itemname

Final update. In 4SEF I changed the General options for Flexicontent from Normal to Use Joomla SEF, reindexed the site and now get non-sef and sef links that work:

non-sef url: group.cruiseand vacationdesk.com/index.php?option=com_flexicontent&Itemid=2752&cid=24&id=1285&view=item

sef url: group.cruiseandvacationdesk.com/cruises-...m/1285-save-up-to-10

This looks to be resolved now.

great news