If the cold water tank is still in use, then, as Steptoe says, the boiler has zero effect on the hot flow rate - it is purely by gravity (from the water level in the cold tank to the tap you open).
If you have a "power shower", it has a pump inside it (easy to tell, `cos they`re noisy things!) - which would fit with a gravity system.
The only options to increase the flow are:
1. replumb the hot water with 22mm pipework - awkward and challenging for DIY.
2. install a pump on the hot water pipe - not cheap, and you may need to increase the size of the COLD water tank to "keep up" with the increased flow.
3. Move the COLD water tank higher up in the house - the higher it is, the better the flow.
4. Fit an unvented cylinder - the most expensive option, short term........but, in my opinion, the best solution.
Problem is - a kitchen sink MUST have the cold water supplied from the rising main - usually entering at 2-5 bar, depending on your location....
Then you`ve got your "gravity" pressured hot water - if memory serves, every 33 ft head of water equals 1 bar - so your hot water is nowhere near the pressure of the cold. This can be a massive problem when you install a mixer tap - the cold has so much pressure, it can effectively block the hot water from mixing properly ( imagine a car waiting to get out of a side street, into a fast flowing line of cars - the spaces between the cars are big enough for your car to fit in, if you were already at the same speed as them, but because you`re stationary, they`re creating a "solid wall" that stops you entering the flow......)
HTH
KME