Since the Grand Canal appears to connect Dragaera City to the western coast, my assumption is that the flow (insomuch as a canal can flow) of water in the canal is westward.
However, Steve told me that the Lesser Sea of Chaos is drawing water into itself via the Canal in Vlad's time:
The Grand Canal runs through the county of Merwin, home to Loraan:
Steve's Map has a dotted line indicating the borders of Merwin, but no locations within it are labeled.
In Athyra, Vlad visits a small village in this Barony, which is located about 1.5 miles south of a cliff referred to as Smallcliff.
To the west of this village, about 3 miles or so, is a place in the road referred to as the Curving Stone, which appears to be very near to Loraan's manor house.
Although its direction is never stated precisely, I believe there is another cliff to the south, named Bigcliff.
Since the river comes in from the right, and then turns south, Savn is facing south, which puts the Brownclay River to the west.
That would put Loraan's keep (Sitria) to the west as well:
To the east about half a day (25 miles, I'll guess), is the town of Whiterock
which appears to be located in a different county
I guessed that Sitria is located about the same distance to the west of the village.
Finally, in the very first passage above, Paarfi refers to the nearby village of Canal, which, based on its name, I assumed was located directly adjacent to the Canal. I guessed it was a similar distance due north of Sitria.
Barony of Loraan
On the photos of Steve's Map, there is an unlabeled point in the far northwest of the region labeled as Merwin that lines up almost exactly with where I would expect Sitria to be based on the above, so I located Sitria there, the nearby city of Canal due north and directly on the Grand Canal.
This resulted in Whiterock appearing slightly within the area Steve had labeled as Merwin, so I pushed it a little bit further east until it was outside of Merwin.
Savn believes that the Brownclay River runs south all the way to the ocean. Steve shows Merwin almost directly north of Mount Blackbird, so I drew the Brownclay River flowing south into the Elbow River.