“Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God.”
Paul was writing to Rome from Corinth. He had Tertius of Iconium write this while he dictated. Paul had established a number of churches around the Greek seas in the decade leading up to the letter. Rome was the then undisputed capital of the 'known world.'
Paul's chapter is structured as to submit to government, love your neighbour and to put on the armour of Christ and eschew fleshly pleasure. This verse is about submitting to government. It does not have implications regarding the US Revolution or Democracy. Submitting to English Government or the Revolutionary government does not extinguish ones duty to Christ. Neither does voting in a Democracy.