Yes you can caulk but in reality you should also be using chimney flashing which gets attached to and sealed to the chimney and then gets bent over the j channel.
Flashing a fieldstone chimney along siding.
Next comes the counterflashing.
If this is running along the side of the house and not by the roof then maybe caulk at this point.
A second layer of metal is embedded in the chimney mortar joints and folded down to cover the top of the step flashing.
The project is ocean front and it has become a point of discussion as to how to prevent water from penetrating when we get the sideways rain that we do.
Anyplace where the roof plane meets a vertical wall such as a dormer a chimney or a split level roof flashing is necessary.
I ve looked around a bit and all the details i can find only deal with chimney roof flashing.
Along the bend at both ends so that the flashing bends around the chimney at the bottom and overlaps at the ridge.
Pieces of 18 inch wide flashing installed prior to the brick work but on top of the house wrap in a stepped fashion periodically laying on top of the lapped upper portion of the siding to get the water back to the exterior of the wall is more along the lines that i would be thinking of.
Sections of l shaped sheet metal are woven into the shingle courses and lapped up the side of the chimney.
Once the pan flashing is in place nail it to the roof sheathing and lay the shingles over the flashing.
On each end of the pan flashing cut about 1 1 2 in.
Proper flashing around a chimney includes two layers.