Proper flashing around a chimney includes two layers.
Flashing a fieldstone chimney along siding.
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.
On each end of the pan flashing cut about 1 1 2 in.
Next comes the counterflashing.
The other measures should have been taken before the siding was installed.
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.
The house will receive a cement style siding panel with no inside corner trim against the brick.
Along the bend at both ends so that the flashing bends around the chimney at the bottom and overlaps at the ridge.
If this is running along the side of the house and not by the roof then maybe caulk at this point.
I ve looked around a bit and all the details i can find only deal with chimney roof flashing.
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.