Adding gears to my grandson's 12" bike
If your grandson is that young, he's likely to have trouble keeping up with you no matter what bike he's riding. It may be that it's your expectations, not his bike, that should be modified.

It seems really unlikely that you could retrofit a derailleur onto his current bike. A frame that small won't have room for a wider rear-wheel assembly. Mounting rim brakes would be tough if the frame isn't already set up for it. Even if you did succeed, he'd still be driving it with eight-year-old legs and an eight-year-old's heart and lungs.

Might you consider a tagalong bike, mounted to your bike? Your grandson might balk at this if he's used to his own separate bike, but it would ensure that he keeps up with you.