The control of flow, level, pressure and temperature can be very interesting and has been making a good living for me for over 25 years. Some writers here are on the right track, but I would like to briefly explain a few concepts so that any confusion is not propagated on this thread.
First, flow is related to pressure, but more specifically it is related to pressure drop. If there is no pressure drop, there is no flow, period, as Bill F pointed out in his example.
Flow is measured in units like gallons per minute, but the capacity of a valve, regulator, orifice or any opening, for the amount it can flow, is measured in units called Cv, (liquid), Cs, (steam), or Cg, (gas). The Cv is equal to the number of gallons of water that can pass through an opening in one minute at a 1 psig pressure drop, (psid). For the flow to increase either the opening must be enlarged or the pressure drop must be increased. In a closed system, simply increasing the pressure does not necessarily increase the rate of flow. You have to increase the pressure drop or open up some restriction. As Mike Spencer pointed out there is a limit to how much flow can be achieved through any given opening no matter how much higher you make the pressure drop. That point is called chocked flow. Once you reach that point no matter how much you increase the pressure upstream or decrease the pressure downstream, or both, you just won’t get any more flow through that restriction.
Secondly, increasing the flow of oil through a heat exchanger will help some in transferring the heat out of the oil, but not nearly as much as increasing the efficiency of the heat exchanger. To increase the efficiency of the heat exchanger you can use the most efficient materials, increase surface contact area, remove any barriers to the heat transfer, (clean the surfaces which also increases the contact area), or increase the volume and temperature differential of the transfer fluid, (air or liquid). In our applications, liquid to air heat exchangers are more frequently used than liquid to liquid heat exchangers.
There are some other factors but the bottom line is, to get a better cooling of your oil, you will have better results from cleaning your oil cooler and increasing the air flow through it rather than simply increasing the oil pressure. Mike Spencer and Mustanghammer were onto this.
Be safe and have fun.