How to determine the pressure to output a gas to achieve a particular gas flow rate?
Well, since the pressure in the tank will decrease with usage, you can't ultimately do what you seem to want to do. 

At a given backing pressure, there are equations to determine the orafice size to get a flow rate - google 'choked flow'. Downstream of the regulator, your orafice should be good for quite some time.

For an experimental setup, one would use either a mass flow controller (MFC) to actively control the flow rate, or (much cheaper) one of those little flow indicators with the ball floating in the He (air) stream. Note the second option here is basically an adjustable orafice with integrated flow indicator.