What you have linked is NOT a pump, it is just a pump controller. (a device which switches a pump on and off as required.) It senses water pressure and if the pressure falls too low, it switches on a pump. It is used in systems that provide a whole of house pressurized system from a simple water tank or well. I don't think it is the product you need.

I think you require a booster pump.

I have linked one on Amazon India for you.

I can not promise if this is a good product, but you will need something like this...

www.amazon.in/STARQ-Autom...

You would use it in automatic mode, so it only comes on when the water starts to flow into the washing machine. You should contact the seller to see if this will be suitable. These type of units have a sensor inside that detects water flow, and starts up the pump when the flow starts, and shuts off when the flow stops. It will depend on your existing system being able to supply at least a very slow flow into the washing machine, which would then be detected and boosted by the pump. If your current system isn't able to open the washing machine's inlet valve and start a slow flow, it probably won't work automatically and would have to be switched on and off manually. (not ideal.)

Another option is to use a 12 volt pressure pump, as designed for mobile homes, boats, caravans and so on. You would need a suitable 12 volts power supply to run the pump. The pump maintains a fixed pressure in the outlet hose, when the pressure drops (because you turn on a tap or the washing machine fill vale opens) the pump will automatically start up and continue running until the tap closes or the washing machine fill valve closes, when it will switch off again.

I have installed one of these 12 volt pumps for a friend who has a 12 volt solar power system at home - the pump runs directly from the 12 volt battery. It provides a good water flow for his washing machine, which runs from a 12V to 240V inverter. Prior to installing the 12 volt pump, he had a similar problem to you - insufficient flow for his washing machine.

I like the 12 volt DC pump option as this system doesn't rely on any flow to be detected to start the pump. I used something that looks like the one in the link below:

www.amazon.in/ATORSE-Pres...

Again, if you choose the 12 volt option, you would need a suitable 12 volt power supply - either a 12 volt battery, and a charger to keep it charged; or a 220V to 12 volt power supply that can provide enough amps to run the pump.

Pressure is important too, not just flow - the water inlet solenoid valves have a minimum pressure required to crack them open.

I live in an area with no town water supply, all homes near here have some form of either gravity feed from a tank, or automatic pressure pump from a dam, well or tank. I know of several local homes where pressure, not flow, is the problem, making solenoid operated washing machine inlet valves unreliable. With a gravity fed supply from a tank not much higher than the home, you can get fine flow if the pipe diameter is wide enough, but the water pathway through the inlet valve is just too restrictive and the valve has a minimum water pressure required to open. These systems are greatly helped by a booster pump of some sort. That is why we fitted the 12 volt pump to my friend's place - his old Fisher and Paykel washer (my old Gentle Annie) was less fussy about water pressure and flow, and worked fine off their gravity feed system, with only about 2 metres head. (tank 2 metres higher than washing machine.) It did take over half an hour for each fill, it was a real trickle.

When that machine eventually died, I gave them a much newer Fisher and Paykel Washsmart, maybe 5 years old? Its inlet valve would sometimes not open due to the low pressure, if it did open, the flow was miserable. I tried a good spare valve but it was the same. Installing the 12 volt pressure pump fixed the problem, it now fills in a few minutes, the old machine used to take over half an hour to fill.

If fitting a booster pump to a slow town water supply doesn't help because the town supply just can't supply water any faster, then it is still possible to make a solution - a small reservoir or buffer like Henene4 mentioned above. Use a float valve to fill a small tank or cistern (100 to 200 litres would be my suggestion) and the tank can fill very slowly, it could even take hours if needed. Then a pressure pump (12 volt or 230 volt) can take water from the tank/cistern and feed it to the washing machine. A toilet-cistern-style float valve would control the flow of town water into the tank/cistern, so it never overflows. The water level in the tank will fall when the washing machine is filling, and slowly refill once no more water is being taken from it.