Richard Brooks would probably be the only possible higher end source. I think they are in the design district.
There -was- a cool little place in DeepEllum, but I don’t know if they ever reopened. Fabrique, near the Plano outpost for Central Market was my “go to”, but they closed up shop about a year ago.
You might check out Sew It Up Bernina in Hurst. They don’t have a lot of fashion fabric, since their customer base is more into quilts and accessories like tote bags. But Lorraine started the business as The Grapevine Collection - with luscious heirloom sewing fabrics (batiste, linen, etc.)
Some quilt stores have small selections of rayon and/or linen. But I’d call before going to ask.
I think most of the fashion fabric business is now online. Mood, Fabrics.com, etc. unfortunate, since touching the fabric is the fun part, but as the guy that owned SuperTextiles once told me, the wholesale sources for fabric in the US have all but disappeared, as manufacturing has been outsourced to Asia.