CBR gives tons of statistics at http://www.cbr.ru/eng/statistics/?Prtid=svs
Take a look at "Net Inflows/Outflows of Capital by Private Sector" and “Balance of Payment” in different representations. I warn you ahead that it’s not that clear from the data what moves where.
There are several reasons for capital flight
1) Dollarization and flight to safety. That is related to a high inflation and bank runs in the past 25 years after USSR collapse. Russians do not fully trust in ruble and local financial system. A lot of Russians hold foreign cash, mainly dollars and euros.
2) Sanctions. Because of the Ukraine issues the West put sanctions and effectively closed its financali market. So Russian banks and enterprises cannot refinance and have no way but to pay debts. Paying debts is like capital flight.
3) NX = S – I. Russia has chronic CA surplus which means capital outflow. It lasted for years. See http://goo.gl/zBA0Eq
If you have insufficient investment demand inside country for its savings that means capital outflow. That is related to 1) also.