This or That か

か only offers a choice between things, not a choice between actions. Choosing between two verbs needs 〜たり〜たりする or a different construction entirely, this か is strictly for nouns standing in for each other.

どちらか tacked on after the か pair spells out explicitly that a choice still needs to be made between them, “one of the two.” It’s not required, メールか電話をします already works fine, but どちらか makes the sentence read less like a vague list and more like a genuine either-or decision.

In メールか電話かどちらか, the か after メール and 電話 marks the two alternatives (“email or phone”). The final か is part of どちらか, meaning “one of the two.” So the sentence has three か’s, but the last one is doing a different job.