With some difficulty but you could submit to a web process to fetch back filled in keys by returning FDF.
Assuming this is an Acrobat form and not a LiveCycle Designer form, you can't do it, at least not directly.
One alternative is to export the values from the DB to a text file and then read that file from the PDF and use it there, but that would require a complex set of scripts.
As was already indicated, you can use FDF. If your solution only needs to run on Acrobat, and not the free Reader, you can also use SOAP. See here for a simple example: Getting a Serial Number Into a Form Using SOAP - KHKonsulting LLC