SPOILER ALERT
The flask is under some thorn bushes that you can remove with your stone scythe. Dip into the river to fill with water (only have to do that once).
I counted a total of 13 trees (I am not sure whether they are always the same, but I think that they are.)
10 trees that need water in the area you can reach without building any bridges
2 trees in the area reached by bridging the chasm that has the rainbow and the stone that says "take care of the trees"
1 tree in the other area reached by bridging the other chasm
When you water the last tree, the screen will move automatically to show the opened path to the village.