In the sentence "Brianna was voted the co-captain" is "was voted" a linking or action verb phrase? I believe it is action and "co-captain" is the direct object (co-captain as a title/position), but it is difficult to explain to students as they view it as Brianna = co-captain.
If you change the sentence into active you get: They voted Brianna co-captain with the structure verb, direct object, complement to direct object.
This is not the structure of a sentence like "My father is a teacher". So I wouldn't say "voted" is a linking verb.