If you dont know the chemical structure of the dye, I think, it may incalculable.

if you ask the necessary formula for teoretical COD, it may be given as follow

CnHaObNc + (n+(a/4)-(b/2)-((3/4)c)) O2----------- nCO2 + ((a/2)-((3/2)c) H2O + cNH3

The chemical ixygen demand of the dye, can be calculated with cod determination protocol like the other organic materials using potassium dichromate as the oxidant. You can find the procedure in the literatures. 

Maybe this attached file is helpful for you.