Roads are the best way to increase your cash flow. Each worked square with a road produces at least one gold, and often more. Whenever you improve a tile (with, say, a mine or irrigation), you should routinely add a road as well.
In addition, your tax rate will affect cash flow. Set this by hitting F1 to go to your Domestic Adviser. There's a slider that allows you to strike a balance among science, tax, and happiness spending.
Yes, government types can affect cashflow. If your cities are generally over population 6, it probably is time to think about monarchy or better. To really increase revenue, Republic and Democracy are the way to go, but those gov'ts also do charge you more for unit upkeep, so there's some tradeoff: higher revenue and growth in exchange for higher costs.
Mines affect cashflow only indirectly -- either by generating cash in an associate road, or if the owning city is producing "wealth". In a pinch, you can ask cities that produce lots of blue shields to make "wealth" to increase your cash.
Hope this helps.