My scalp is the same. Day 3 is about when I'd consider it "dirty". I've found that there really is no alternative to just washing it. Dry shampoos are a temporary refresher but they seem to make my scalp dirtier even. Nothing you apply to a dirty scalp is going to cleanse it. Believe me I have tried it all in a quest to stretch my flat iron jobs. There is nothing... it just has to be washed.
I also hate how my hair begins to look by about day 3 so I generally wash and iron my hair about twice a week nowadays. I'm not seeing any ill effects since i dc with heat frequently.