"I suppose it's likely a typo and the correct year is 1699. Dickson's reference is not to the current collected writings and letters, but to the _Leibnizens mathematische Schriften_ edited by Gerhardt: Band 3, vol. II, p.601."
Your hunch is right. The letter from Leibniz to Joh. Bernoulli is dated 28 July 1699.
BTW, I don't think that the Gerhardt edition is accessible online, but I'd like to be proven wrong. The Goettinger Digitalisierungs-Zentrum, as Robert Tragesser points out, has lots of Hilbert, but I don't think you'll get Gerhardt (or many of Leibniz's mathematical writings for that matter) there. As far as I know, the best online clearinghouse for all things Leibnizian remains: