There are at least 2 reasons why dandruff can happen after a semi-permanent straightening.
1.The product that adheres to the hair can also adhere to the scalp. As the scalp skin cells shed, the product sheds off as well, creating large flakes. It is fairly impossible to keep every speck of product off the scalp, so the product that ends up on the scalp gets cooked on during the flatironing.
2.The semi-permanent straightening product can upset some people's skin and start them on a path of flakiness that can last months. Not sure why.
Either way, the quickest way to resolve this is:
1.Prior to shampooing, with the hair totally dry, exfoliate the scalp using a scratchy comb, brush or whatever works. Scrub the skin, lift up the flakes, then shampoo and condition as usual. You might need to exfoliate the scalp prior to the first several shampoos as the skin can take a week or so to shed and release the stuck on product.
2.Use a dandruff shampoo that does not contain Sodium Chloride. After exfoliation, shampoo with the dandruff shampoo of your choice. Really work it into the scalp and then let it sit for several minutes. Rinse and condition as usual.