Is it possible to store the Site Address url and List Name in string variables so I don't have to hard code these values in my Flow?
Yes, it is possible.
But it is recommended to take use of Array variable to store the Site Address and the List name seperately:
I can setup the variable array fine but it doesn't seem to allow me to use it during design-time. When I tried to use the variable to retrieve the Site Address and List Name during "update item" action (I want to update the value of a column on the list), it errors out, "Cannot evaluate the parameter 'dataset' at design-time; it is empty or has a runtime expression". The workaround would be hard code the Site Address and List Name every time I need to "update item", since I need to update the list numberous times during the whole flow, using variables would be nice. Aslo when I am ready to export this flow to another site, I don't need to modify the flow to change the Site Address numberous times.
Unfortunately I don't have the perfect solution as I wanted, but I have a workaround. Export the flow to package (.zip), open the zip file and edit the definition.json file, specify the new site addrss url, the new list name etc. then import back. I used 7-Zip to open and it opens the flow definition file in Notepad for me to edit.
Found any other viable way to do this? I have a flow that runs on main site and needs to move files to different sites depending on variables. But I can't update properties since I get the same error you have.
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I'm using the workaround solution and didn't have time to check and rewrite my flows. So, unfortunately, I don't know now. But I will check it soon.