I worried a lot and tried everything when Scottie was 5 months old. I tried
oatmeal bathes, grinding up my own oatmeal powder
using non-fragrance natural shampoos
changing diet to higher quality grain-free kibble
brushing the hair daily.
Not really sure if any of the above helped. But with time, after 1 year, his skin suddenly cleared up. So I'm not sure if it was a puppy thing or a health thing.
When I got Casie and she had the same dandruff/dander issue at 5 months. It's pretty gross, I didn't want to give her scratches because it would snow! I figured she'd grow out of it just like Scottie did, so I didn't bother with the oatmeal bathes etc (it was very very messy and some claim that the oatmeal isn't good for dogs' skin lol). But I believe she did grow out of it. Right now at 1.5 years, her skin seems to have cleared up.
And yes, I apply conditioner when I bathe them.