Only Illustrator and Flash (now called Animate) understand Symbols.
Forget the Symbols. You would just need to drag artwork to the Libraries panel. Here is documentatrtion for creating libraries in Illustrator:
Here's documentation for CC Libraries in InDesign:
Thanks for your response. I should have not used the term "symbols," since that has a specific meaning. I'm creating icons for use in an InDesign document. I am doing so by creating them in a master Illustrator document, each with 1000pt square art boards and adding them into my cloud library. I then place those icons into InDesign. If I want to go back and swap out the object in InDesign with another identically sized object (different shapes/colors), I want to just relink to the new cloud library icon (like I would if I replaced the link with an updated artboard using the "old fashioned" method). How do I go about doing that? It seems like I have to place a new object from the cloud library into the document then rescale and reposition it, versus relinking it to a new object in the cloud. Does that make sense?
If you had edited one of the icons, the link in InDesign would appear out-of-date and you could update it.
If you want to replace it with a new icon, you need to place the new object, rescale and position it.