If your going to stay with the flat bar, some fine tuning may be in order.

Make sure that your bike fit doesn't put too much weight on your hands and arms. You should be able to remain in your riding position for a short while with nothing but your finger tips on the bar (all your weight on the saddle). If your saddle is tipped too far forward, you may find yourself having to support too much of your weight on your hands and arms to keep the butt from sliding forward.

Do not ride with your brake levers level with the ground......they should tip down (rotate forward) untill they are parallell with your lower arm when you are in riding position. This will provide a more comfortable angle for the wrist.

Move your hands often..........just because they are flat bars does not mean that you have to ride with the hand in the same place all the time. You can rest the hands by grasping the end of the bar from the side. You can move the hand in and out. Most importantly learn to relax the hands as it is not good to ride all the time with a death grip and the fingers always on the levers ready for a panic stop.

As others have mentioned, riser bars with more rearward sweep 5 to 8 deg will probably be more comfortable........and they will be wider.

As a last resort, a carbon bar may take that last bit of objectionable vibration out of the hands and be more comfortable.

Ride a lot.......