Getting a Russian visa in Hong Kong
Getting a Russian Visa in Hong Kong for travelling the Trans-Siberian Railway shouldn’t be a problem. With the required documents correctly filled out, and assuming that your reason for visting Russia isn’t listed as espionage, terrorism or political assassination, you should be able to pay your fee and receive your visa within the allotted time.
As a UK passport holder, getting a Russian visa was a relatively painless affair. If you can negotiate the almost comically foul-tempered staff that work at the Russian consulate in Hong Kong, then whatever passport you carry, you should likewise have no problems getting everything in order for you Trans-Siberian trip.