Hi Lizzy,
Yes the heat from flat irons (and any iron that gets really hot) can be drying. You should use a heat protectant that stays in, before you dry your hair. The best one I know of is Bliss by Nioxin. It conditions, rebuilds and protects hair even from ultra high temps. It is sold in salons.
There are others that you might find in the stores.
In addition to that, using a smoothing serum will give a smoother, silkier finish. (ARTec has Kiwi Blow Serum, Nioxin has Reflectives Silk Elixir) You will find similar items in the stores. I haven't found any as good as these or that last as long - since they are concentrated.