This pattern only use one dmc color 3866, I'm not sure which color fabric is best for this pattern because I never use fabric other than white aida.
I'm thinking of using black, but I really not sure whether the result will be good or disaster.
I think it would look lovely on a green background. Or even a neutral color like tan or light brown, as long as it is somewhat darker in shade than the thread.
If you are more comfortable sticking with the white aida, you could always use a different darker thread color such a black/brown/navy blue/dark green
I've started a Parolin design on natural dark linen and MDC 3865. whis is whiter than 3866.
Consider that the design is big so probably you need to buy fabric. Go there with the floss and try the best fit. Use thedarker farbic in order to see better the design. Good work