There are a number of ways you can improve your flexibility:
(1) Stretch more. Use a variety of stretching techniques to stretch the muscles in your chest and arms. There are even videos available that show ways to stretch all the muscles. For you, you would want to focus on your chest, forearms, triceps, biceps, and shoulder muscles.
(2) Use a piece of elastic to help you stretch your arm. A number of these devices can be purchased from baseball supply stores.
(3) Consider taking yoga classes. Yes, I know this is not the most masculine thing to do; however, if you do not know already, a large part of yoga deals with improving flexibility thru stretching.
(4) Consider taking martial arts or ballet classes. Both of these types of activities focus on improving flexibility. In fact, a number of professional football players including Herschel Walker have taken ballet classes to improve their flexibility. If this can help them, it can definitely help you too. These types of activities are also good because they let you cross-train your body in a different way.
Hope this helps,