I think that will be the simpler option really if you don't want to have to deal with file formats, SD cards and filesystems, and using a flash chip this way will be much easier to understand and easier to get something working in real-time. And if your intent is not to develop a full-blown audio player, but a dedicated one as I understood it, that's perfectly fine. Of course just keep in mind that changing the audio content will require a "maintenance" and the user won't be able to do it themselves, which is not necessarily a problem here. (Note that it could still be implemented later on if you're using an MCU that supports USB, but that would obviously require more work...)
In Audacity just use Export / Export Audio, select "other formats", then "RAW (headerless)" for the header, and then the encoding you want for the samples (ideally the same format as what you'll directly send to the DAC).