I’m gonna quote Joe DeFranco on this one. This is taken from his site.
A reader asked him the very same question, elbows flared or tucked?
It?s not that one is better than the other; it depends on your training goal. Most bodybuilders advocate the ?flaring elbows? version because benching in this (horizontal) plane does recruit the pectoralis major to a greater extent. (It?s important to know that joint position dictates muscular recruitment patterns.) So, if your sole purpose for bench-pressing is to put some muscle on your chest, this form is probably your best bet. I have found this version to place more stress on connective tissue and the Acromioclavicular joint (AC joint), though.
The ?elbows tucked? version was originally popularized by powerlifters. This is how I teach all my athletes to bench press as well. I coach them to lower the bar to just below the nipple line. The upper arms should be at a 45-degree angle in relation to the upper body in the bottom position. I then coach them to accelerate the weight upward in a straight line. Bench-pressing in this manner is less likely to tear connective tissue surrounding the shoulder joint. Benching in this (sagittal) plane recruits the triceps and latissimus dorsi to a greater extent, while the pectoralis major is less involved. It is also more specific to the pushing movements required in most sports ? offensive lineman pass-blocking, hockey players checking , etc.