Anyone can say "God gives me authority to teach" some may be right others not so.
My personal opinion is the question lacks any clarifying power. To know if someone teaches by Gods authority is to check their word with the word of God. If they match up then great if they don't then reject.
There is no quick question that reveals the answer to your question.
Act 17:11 These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
In my experience this is the only way to know by who's authority one speaks.
Many genuine people who are open still do not teach by God's authority.
Just my 2 cents, take it or leave it.