The TFA version was a nylon with a printed pattern on it. Unless you order a custome print job, you won't get an EXACT match, but you can come close in general look, especially with herringbone pattern material.
Avengers might be more difficult. Some people think the fabric is textured, others are certain it is a printed on pattern. The neck area of the mask appears to be a custom print, but the body I think is questionable. A costume designer at Disney swears it is a textured fabric, people here think it's a printed on pattern. No idea myself.
There was a reference to a sports fabric in another thread, try searching 'definitive captain america'