I want to get a Russian tourist visa to take the Trans Mongolian express from Beijing. However I will not book my train tickets in advance.
Can I book flights to get my visa, cancelling them afterwards to enter/exit Russia by train?
You do not need the tickets to obtain your visa, you only need a confirmation that you'll be hosted as a tourist. This usually is a hotel booking voucher or some similar document, you should contact your consulate for more detailed information.
All in all, hotel booking can be easily canceled, usually without any cost, if you do it in advance.