If it's a 3D procedural you are using, parent the ... ugh.. the name escapes me right now.. the green box that appears when you apply the texture to the cloth. Parent that to the cloth. (yeah, I suck at explaining things)
If it's a 2D texture, you can parent the 2D placement node to the cloth if it moves around. Since it's a flat texture, it should "swim".
Hope this confused explanation helps. 