Many people notice troubling changes from their scalp when they have telogen effluvium. Some notice itching. Others notice flaking when they're reasonably sure that they've never had dandruff before. Someone might say, “as if my horrific hair shedding is not bad enough, now when I look at my clothes to pick off all of the spent hairs, I now notice little flakes sitting on my shoulder. It appears that I now have dandruff and my scalp is itchy. I've never had a dandruff issue in my life. Is my dandruff related to my hair loss? Will fixing the dandruff improving the shedding?”
I had some flaking with my own telogen effluvium, but I was told that it was dry scalp instead of traditional dandruff. Both of these conditions cause white flakes and itching. In my case, my scalp dried out because of some of the over-the-counter topical treatments that I was trying to stop the hair loss. Telogen effluvium is usually caused by some sort of medical condition, stress, or change that happens internally to the body. In turn, the body attempts to conserve its strength by changing your hair cycles to the shedding phase. Dandruff usually does not fall into the category of a telogen effluvium trigger, unless it is an allergic reaction or an inflammatory response to something. Most of the time, triggers are things like illness, medications, pregnancy, dieting, etc.
Inflammation to the scalp and the hair follicles being so active can definitely cause itching. (And there are some people who get some pretty heavy inflammation on their scalp as the result of all of the shedding that is hitting the hair follicles all at once.) Usually, though, this happens after the shedding begins. It is not the cause of the shedding. I'm not a doctor, but my research has shown that there are some inflammatory conditions of the scalp that can cause hair loss, but they're relatively rare and they typically feel much more painful than typical itching.
I actually found that dandruff shampoo helped my shedding somewhat. I think that it was because of the anti-inflammatory properties. I compared dandruff shampoo with baby shampoo, regular shampoo, and shampoo that supposedly was specifically for hair loss. For me, the dandruff shampoo worked the best, although it just helped a little. It did not solve the issue. Again, I think that it was just tackling the inflammation that was caused by all of my shedding. I don't think that it was treating my hair loss, as once the TE cycle starts, you just need to keep your scalp healthy, address inflammation, and wait for your hair cycles to reset.
I should mention that there is another hair loss condition called androgenetic alopecia (AGA) that is caused by reactions to androgens. Sometimes, you do see dandruff with this condition also, especially when there is excess sebum. So that is also a consideration.