Is it possible to use a form to lookup and display data?

Can I use a jotform to retrieve data to display to the user?

If I had a database of data, could a form be used to select or enter search criteria and a Flow integration retrieves that data from a database and then presents it to the user?

You can import data as submissions of your form:

Import-App-Easily-Import-Your-Excel-or-CSV-Data-into-JotForm 

But, as far as I understood, you meant the other data. There is an option to show the data, but, unfortunately, search option will not be present.

So, you need to create a Google Spreadsheet (I have used it as example, the idea is to get it's embedding code) and embed it to the Text field of your form:

Hope this helps!