A lot of terrible advice in this thread.
Generally if you are vegan and you are experiencing hair loss, dandruff or any type or dry skin you are deficient in specific nutrients. Vegans with this issue are most often deficient in one of several key nutrients.
Essential Fatty Acids, not just omega 3 fatty acids, but omega 6 fatty acids as well. Only you can tell if you are deficient in these nutrients by examining your diet. Flax seed oil is usually necessary for most vegans to supplement with. I would recommend getting the brand Udo's Choice which is organic and has cold pressed flax seed oil as well as other cold pressed omega 6 oils in a good ratio.
Zinc Deficiency is also a common problem vegans experience which can result in your symptoms. This nutrient is tricky as it competes with copper for absorption by the body. Many vegans believe they have adequate zinc intake, but similar to the essential fatty acids a correct ratio of zinc and copper is required by the body. Most
vegan foods have similar copper and zinc levels but much more zinc is needed by the body, the correct ratio being closer to 7 or 8 to 1 zinc to copper. If you can not add foods that have a large ratio of zinc to copper to your diet I would recommend getting a zinc supplement. I added organic grass fed eggs to my diet when I discovered I was zinc deficient as a vegan, but this may not be necessary as there are vegans that exist without these issues. Also keep in mind that phytates present in many whole grains and legumes bind with zinc and inhibit absorption by the body.
The Symptoms of these deficiencies can be treated by applying coconut oil to the problem areas daily. However, this is not a permanent solution and the symptoms will return if you stopped application for a while. I do not advise masking the symptoms with coconut oil or other products as it can make it difficult for you to tell if you have resolved the issue nutritionally. I would only do this if the problem is embarrassing enough that it is causing you undue stress, as stress causes the body to deplete zinc.
You mention you are taking a calcium supplement and a multivitamin. Calcium can exacerbate zinc deficiency and a balanced
vegan diet should never require calcium supplementation. I would also be wary of your multivitamin as many contain copper and are not designed for
vegan diets. Examine your diet and find out what nutrients or minerals you are lacking in and if you cannot add a food then supplement a high quality supplement for that specific nutrient and see if it resolves your symptoms.