How do I parse "but that shall be accounted the promised share of this traitor"

Solution 1:

that subject
shall be accounted verb (future passive)
the promised share of this traitor direct object

To account is a transitive verb used in the passive voice here. Cambridge defines it giving a similar example:

account verb [T + obj + noun/adj] (JUDGE)
to think of someone or something in the stated way:

  • She was accounted a genius by all who knew her work.