I've actually checked my blood pressure on a home monitor after a bottle of 14% ABV red wine, and it was far lower than before I indulged.

It will do in the short term. A doctor friend explained it to me once.
Alcohol thins the blood in the short term but the body, always trying to equal things out, will react by trying to make the blood thicker and use vitamins and minerals in the process. This will of course be an over-reaction which will vary in severity of the amount of alcohol consumed and adds to the hangover effect while the body rebalances. The more often you drink the more the body will get used to it and react less, resulting in small hangovers and more blood reaching the skin (due to the thinning which does not decrease with regular alcohol consumption only the body's response)
The 'flushing' may thus be merely a sign that you are drinking a lot and your body is getting used to the effects of alcohol in the body. Long term it can lead to alcohol induced Rosacia which can, rather humerously, make the nose go red and itchy when drunk. As a result the french sign-language for drunk (and used in common discourse by everyone as a signal to another person) is to put a fist-like hand on the end of the nose and then rub the nose from side-to-side as if itching it.