If he's tall/big enough to ride a full size 20 inch bmx, then i'm guessing he's still not gonna be that tall (compared to a full size adult) in which case you want to go with a shorter top tube, around the 19 inch mark I would say, and chainstays as short as possible, sub 14 inch ideally, some slightly lower bars (around 6.75/7 inch rise), and a short stem should do the trick.
How tall/big is he, i'm guessing he'll want a 16 inch or 18 inch wheeled bmx if he's pretty small:
Good 16 inch choice: http://www.mirrabikeco.com/blend_16.html
If he's tall/big enough to ride a full size 20 inch bmx, then i'm guessing he's still not gonna be that tall (compared to a full size adult) in which case you want to go with a shorter top tube, around the 19 inch mark I would say, and chainstays as short as possible, sub 14 inch ideally, some slightly lower bars (around 6.75/7 inch rise), and a short stem should do the trick.