I've only heard it - with its apparent use in this case - in phrases about knowledge specific to someone or something, as in:
かみのみぞしるあめのみぞしる。
I would normally - with my low-level understanding of Japanese - use を and say for example:
それはかみのみをしること。
I've not found any info on Google. What is the function of ぞ and where else can it be used?
Nobody uses it now, because it is a piece of grammar from classical Japanese. The final particle ぞ is a descendant of it, and otherwise only remains in sporadic idioms: ～のみぞ知る, どうぞ, これぞ, よくぞ, 何するものぞ etc.
By the way, its meaning is not related to を. In old Japanese they don't have consistent nominative or accusative markers, so it could be a subject or an object.
かみのみぞしる
It is only god(s) that knows.
