Picoquant has a list of diffusion constants for some fluorophores:

http://www.picoquant.com/images/uploads/page/files/7353/appnote_diffusioncoefficients.pdf

Texas red isn't on the list, but it does have some other common fluorophores you might use.  

I also don't know how exact a value you need.  For example, maybe Rhodamine 110 value could be used as an estimate

thanks! I think Rhodamine 110 can be useful too!

Please find attached article. Page 2947: "The corresponding flux (fmolcm–2s–1) was then calculated from the Fick equation (Eqn1), where D is the diffusion coefficient for

Texas Red (2ϫ10–6cm2s–1) (Saylor, 1997)"

Hope this will help

Best