Have you considered rearchitecting your approach? You're not going to be able to gracefully do this with a Configuration - be it XML, table, environment, or registry key. In the simplest case, a table, before you could even start your SSIS package, a process would need to update that table to use the current date. A scheduling tool like SQL Agent can run SQL Commands. If you're going the XML route though, you're looking at a tiny little app or PowerShell command to modify your configuration file. Again, that's going to have to modify your file every day and before the SSIS package begins as it sets values once in the beginning and never consults the configuration source again.
You could use an Expression in SSIS to use the current date as part of your flat file source's connection string but in the event you need to process more than one day's file or reprocess yesterday's file, you're humped and either have to manually rename source files or change the system clock and nobody's going to do that.
A more canonical approach would be to use a Foreach (file) Loop Container. Point it at the source folder and find all the file(s) that match your pattern. I'm assuming here you move processed files out of the same folder. The Foreach Container finds all matching files and enumerates through the list popping the current one into whatever variable you've chosen.
See a working example on