What are the flaws of the British system of government according to the authors of the Declaration of Independence? What ought government to be...

The Declaration contains a litany of grievances that set forth the American colonies' reasons for a separation from Great Britain, but one of the most important reasons is stated in the Declaration's first paragraph and often goes ignored, or at least not adequately considered:

. . . all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,

The revolutionary part of this section is not that "all men are created equal," by which the framers of the Declaration really meant all white men who own property are created equal, but that governments exercise their powers because of "the consent of the governed."

For King George III and other monarchs in Europe in the latter quarter of the 18thC., the most radical statement made in the Declaration was not that the King or Parliament had instituted unjust taxes--although that did make the average merchant colonist mad--but that colonists in America were arguing that a ruler governs not by divine right, which was the prevailing belief at the time, but that the people had the power to consent to be ruled by someone.  This sentiment rattled the cages of every monarch from Great Britain to Russia because it undermined the foundation of their right to rule.

After undermining the concept of Divine Right, the Declaration sets forth the specific injustices of Great Britain against the American colonies, beginning with Great Britain's failure to consent to laws that benefit American colonial commerce and ending with the accusation that Great Britain has created unrest among the indigenous people and the colonists.  The Declaration's list of grievances comprises the whole of Great Britain's failure to govern its American colonies properly and, more important, fairly.

As a last comment, I will add that several of the founding fathers came to the conclusion that it made no sense for a small island (Great Britain) to rule a vast continent like America--and this was even before anyone knew exactly how vast America really was.