I don't chemically straighten my hair, but in general, you should stay away from mineral oil and petroleum (as others have mentioned) as they coat the hair and clog the pores of the scalp, making dandruff worse and also causing dryness as they prevent moisturizing ingredients from penetrating the hair.
Also, a note on sulfates (and I am referring to sodium laurate sulfates). It's not that they are bad per say, it's just that the can be drying, especially if you wash your hair often, however, if you use a conditioner or styling product that has silcones (and LOTS do, especially drug store brands, or anything that claims to smooth; think Pantene, Dove, etc. even Aveda and other high-end brands) you need to shampoo with a product that has SLS otherwise the silcones won't be removed and they will buildup. HTH.