Well, this is very interesting.
Meanwhile, I found an interesting publication:
http://publications.iupac.org/pac/1996/pdf/6809x1689.pdf
On page 1696 there is a diagram with the relevant reservoirs of chlorine.
The ocean contains 26 Zg of Chlorine and the only relevant source is the Earth's crust, from which 158 Tg/ a are transported into the ocean.
Trying to get an estimate how long it would have taken to reach the actual Cl mass found in the ocean I get
26 Zg / (158 Tg/a) = 165 Ma
This seems way to low, especially since the Cl content of the crust was probably even lower in former times. They also state that the chloride content of the oceans stayed almost constant during the last 600 Ma. I don't understand how this is compartible with their model.