“Chitty Chitty Bang Bang” is a barely altered reference to the “Chitty Bang Bang” series of British racing cars built in the 1920s. In both cases it’s a reference to the noise the car’s engine makes.
Also, just by the way, as far as I can tell, “Kiss Kiss Bang Bang” isn’t James Bond’s “Japanese nickname”. It’s a term used in Japan and Europe to refer to Bond-style spy movies (it’s a pretty succinct summation of the typical plot). It’s been the title of a few spoofs of the genre.
The theme for Thunderball does refer to Bond as “Mr. Kiss Kiss Bang Bang”. It’s certainly possible that some Japanese refer to Bond the same way, and in that sense maybe it is a nickname. But as far as I can tell, it has nothing to do with “Chitty Chitty Bang Bang”.