How do you carry out flushing of the expansion vessel?

Never heard of doing such. What is the issue and why wanting to flush?

Why would you want to flush the expansion tank. It has or should have a bladder. Water goes in the tank when pressure increases and goes out when pressure is relieved. Unless the bladder is ruptures flushing should not be necessary. Essentially the tank is "flushed" each time you open a hot water faucet.

If you think it is not working properly, replace it. It is relatively inexpensive device and takes few minutes to install. Otherwise, expansion tanks do not require maintenance

Milo