Occasionally a customer asks for a linen tallit.  It’s not a fabric I recommend because it wrinkles easily and requires a lot of care.  There are some more expensive linen fabrics that behave a little better; another option is a blend of linen/rayon or linen/silk and the accents (corners and atarah) can be made of silk.  One thing that must be kept in mind is that no wool may be used as this is “shatnez” and strictly prohibited.