People can have sensitivities to all sorts of things. You can be having environmental allergies which appear as scalp itch/flaking. You may be having a reaction to preservatives or fragrances, detergents or any other of a slew of ingredients in products.
If you notice one or two that give you a problem - look at the ingredient lists. Anything those "itchy" products share is a probable suspect!
Here's a starter list for preservatives: science-y hair blog: Preservatives Which Can Itch
"Dandruff" is a catch-all for scalp dermatitis. Any irritation or inflammation of the skin/scalp causes the skin to "turnover" or speed through the cell maturation process quickly. Sometimes becoming more oily, but often becoming very dry. The skin's barrier breaks down and it cannot keep out chemicals and it cannot keep in moisture. It gets dehydrated and then more inflamed. This gives bacteria and fungi which normally live on your skin a chance to grow more than usual and this can cause more itching. I collected some reading about this issue here: science-y hair blog: Sensitive Skin (Part I)

Some things you might try are Scalpicin Maximum Strength (it's a clear liquid, it's "CG" and easy to apply and contains hydrocortisone to help reduce inflammation and relieve itching). Hydrocortisone cream works too, but takes a little more rubbing in to apply.

Do some detective work on your products. There are lots of us here with a lot of chemical allergies and sensitivities - you're not alone.

The oil-sugar scrubs (or just a scalp oiling with olive oil for 30 minutes before shampooing) can do wonders.

But if none of this helps, you might want to see a doctor. Prescription cortisone creams work for some people. Ketoconazole helps some a whole lot. You'll probably have to attack the itch on many fronts.

But once you get a plan set (and it will take time) - you'll know how to cope.