Yes taking hot showers does increase your bodies blood flow.
When you take a hot shower the hot water hitting your body stimulates your muscles and blood vessels and increases the blood flow throughout your body.
Hot showers also relax sore muscles, looses tight joints and tendons and helps keep your circulation of blood flowing properly.
Hot showers are very good for you and the hotter I can take it the better especially when my muscles are sore.
Soaking in a hot bath also helps increase your blood flow and is nice and relaxing sometimes.