Where would you expect to find gunpowder?
In a cannon, perhaps?
There's a cannon somewhere on Monkey Island.
Forts usually have cannons.
Where can I find a fort?
At the edge of a volcano.
Have you seen any volcanoes?
Or any volcanic looking craters?
From the map screen which includes the south shore, go west to the next map screen.
Herman Toothrot's home, the fort, is at the top edge of the crater.
There's a cannon inside the fort.
And gunpowder's inside the cannon.
But you can't just reach into the cannon.
Push the cannon to makes some gunpowder spill out.
Pick up the gunpowder. (If Herman Toothrot's inside, you may have to leave the fort and re-enter.)