If you have a three-eighths line feeding a three-quarters line and need more water flow will a pressure tank solve the flow problem?

The only solution (I know of) is to increase the size of the supply line(pipe). Water works on volume, both lines have to be equal or supply line has to be larger in order to acheive more flow. Pressure does not increase volume, it's the exact opposite, volume increases pressure. Hope it helps!

As a band-aid solution, yes. Install the tank where the supply line increases. When you use water, it will draw from the 3/8" supply, and whatever the line cannot supply the tank will provide. When the faucet is closed, water will continue flowing from the 3/8" supply until the tank is full again. You will have the same volume of water over a period of time, so if you drain the tank totally or do not give it time to refill you will have the same limited flow as before. It would also be wise to install a chack valve at the inlet to the system. You will need a pressure gauge on the system to set the air charge correctly.

As mantioned above, replacing the 3/8" pipe is the best solution. 3/8" inch pipe is very small and cannot supply a normal sized house. However, if you cannot a tank will provide a temporary solution.