Please recommend if it's better for people who get alcohol flush reaction not to drink alcohol?

Yes: the flush reaction is caused by an accumulation of acetaldehyde, which is a toxic product of alcohol metabolism. This substance is normally only present for fractions of a second, but people who develop the flush reaction have an abnormal enzyme which doesn't metabolize the acetaldehyde properly. This is a chemical which causes damage to capillaries and skin, among other things.