Yes, Zinc for hairloss is a must, the deficiency of Zn is the main cause for loosing hair, even true for animals hair... (a subject of this thread in fact)
Overloading with Calcium has an effect on Zn deficit.
I take Zn almost daily, except Sunday when I take my ampulla of Selenium that the absorption of Se is not disturbed by anything else, like this I am sure there is no antagonism.
Borax I am taking every other day around 100mg at the distance from Zn and MgCl in the evening, also almost daily etc.