It says in the description( for teh lazy ~ 20s-40s ). I have experienced about 20 seconds.
EDIT: Actually, the time to register the "keypress" is almost zero, but the effect is only seen many seconds later. You have to guess what the game state will be in ~20s-40s.
The input rate us pretty crazy right now, the game is barely playable. There was some slow constant progress when there were about 4000 viewers, and they even managed to catch a few pokemon when the view count was low.
> The amount of lag is approximately 20~40 seconds depending on connection quality. After watching the stream for awhile the lag may increase a tiny amount (enough for chat spoilers), refreshing may help in this case.