What amp drill do I need to bore holes in this stump?

I like the stump grinder, but if you want to use the drill check with your local rental place or HD rental. You are probably looking at around a 14 amp.

Rentals are inexpensive..

12 amp minimum, 5/8th inch paddle bit. Low RPM suggested.

Auger bits are only intended for hand drills and very low RPMs

They aren't to be uses at electric drill speeds.

with a properly sharp bit, any 3/8 inch or larger drill should work fine

I can't tell from the picture but it looks like it has a cement collar around the base of the tree and looks lower already.   Being that is what I see, if it is true, then I would sledge the concrete away and put soil over the stump that is all below ground level and seed it with lawn seed. I AM DONE. The rests rots away in 1,2,10,25 years(like I really noticed?)  You may see the occasional sapling shoot out of the ground 5 or 10 feet away which you hit with an axe and cut it underground.  That is a MAYBE.

.Hell, I plant my new tree real close to the original one as the dirt is good  .  The roots will figure they way around it.

Rent a gasoline powered stump grinder.

Rent a gasoline powered stump grinder. You can use the chips for mulch in your Rose garden.

Forget boring holes! Go to the local feed and ranch supply store and buy yourself a bag of nitrogen sodium nitrate. Or potassium nitrate. In the 50 lb bag it'll cost you about $20. Pour some kerosene on the stump. Light it on fire. And then get yourself a coffee can. And start pouring 2 lb at a time on the top of the stump.

The sal petter or nitrogen that you're using. Will cause the area where you put it at to turn white hot. Just keep feeding it your oxidizer. Until you've bored a nice big hollow spot inside of it. 

Then every 5 minutes or so pour another 2 lb down inside the hole. And no time at all you'll have that stump glowing white hot. 

Anytime you have an annoying stump like that oxidize it out of the ground with a fuel like kerosene don't use gasoline!  And granulated saltpeter