Can you explain how this passage teaches that it's a Christian duty to vote? I'm not seeing it.
When we vote, we are selecting representatives that rule over us.
That's how Bible Scripture like that 2 Chron.7:14 directly relates, because it's about choosing God's Way, which when we vote we are indirectly making that kind of choice with what 'kind'... of representative we put in office.
So yes, as Christians we do have the Christian duty to vote.
And in case brethren didn't realize it, Christ's enemies have been making bogus religious laws against Christian preachers teaching about political issues at the pulpit, trying to silence them. Trying to make such a law in the United States affecting religious institutions is a violation of the U.S. Constitution about freedom of speech.