working on your flexibility can be just as important if not mroe than weight training. weight training can hurt you if you do it the wrong way, and their are an infinite number of ways to do it incorrectly. you have to know what your body needs to improve your baseball performance. if you have slow feet in the infield, agility will be mroe important. and kids naturally grow and get stronger and weight training will only directly help your game months after you get into it and you start to see some gains that translate onto the field.
flexibility on the other hand can directly help you very quickly because you can become more flexible very quickly with some diligence. it will help all of your game, including speed, power, and every type of play where you have to contort your body into an odd position.
most of all, flexibility will keep you injury free.
on the other hand, if you weight train and listen to your body and know what you are doing, over time you will be very pleased that you did it, because it will translate with a consistent approach over time. but you have to listen to your body. i know my arm is very fragile and throwing takes its toll enough, so i dont do much upper body work that puts any stress on my shoulder.
also, there are many little things that can hurt your game that result from not listening to your body. for example, my wrist has become very sore and i have to play through some pain in practice and games because i didnt listen to my body when i was doing a lot of reverse wrist curls and wroll ups in the offseason. it seemed very minor, but i should have taken it easy and worked out something else. last year it was my elbow that hurt because of too much tricept work.
once again, flexibility is very important and will not only increase you performance on the field but keep you injury free, which is first priority.