Hi Mark,
I've had the CAL Alpha/Delta combination (actually, I think I still have them in a box somewhere). That's a classic transport/DAC combination that is still well-regarded.
What you'll need is a way of getting the data from the FLAC files to the Alpha DAC. With a CD, your Delta transport sends PCM data from the transport to the DAC over one of a few different cable options (optical, coaxial, AES/EBU, etc). Now you need a device that basically does the same thing as the Delta but rather than reading from CD's it reads from your computer's FLAC files.
So you'll effectively need two things:
1) A repository for FLAC files. This is usually a computer that you have some software running as essentially a media server. You can use Logitech Media Server (LMS), as detailed on this thread, or other software such as Roon. Either way, you point the software to the directory on your computer that contains all of your music files in FLAC format.
2) An "endpoint", or "player" that can interact with the server, receive and decode the FLAC data and then send the digital music data to the DAC. I don't think the Alpha has a USB port, as it's from the 1990's, so you'll need a device that can connect to a network like ethernet to communicate with the server, and also have a coaxial or Toslink data connection that can then go to the Alpha.
Just to provide one example, you could get a Raspberry Pi-based unit like a DigiOne from allo.com. (
https://www.allo.com/sparky-eu/digione.html)
Having a digital media repository has dramatically enhanced my ability to appreciate and find music in my collection, so be persistent and don't get discouraged if it doesn't work the first time.
Michael