I am NOT a Prestige Master but if you look at a player's stats there are many clues.
Firstly COD, irrespective of game mode, has taken approximately 1 day of online play for each Prestige (55 levels of ranking). This varies a little for each COD and for BOII it is perhaps slightly lower.
I am slower, I am averaging 27 hours (1 day, 3 hours) for each Prestige. This is largely because SCORE is messed up in TDM (game objective is kills minus deaths, but Treyarch/COD treats objective like FFA, as kills only), plus TDM reaps fewer points/slower advancement anyway. My SPM is around 175.
SPM and days online
Fast ranking players, who hit SPM 350-400 (this is a typical very fast-ranking player) require 12-13 hours per Prestige. Based on this, Master Prestige should take 5-6 online days for the fastest players, 10 on average and as much as 15-20 for the quite slow rankers. I'll probably take 12 online days, which will put me there in March or April.
Game mode will determine the number of kills. For TDM kills is the primary ranker (bizarrely deaths or kills minus deaths are not factored in, so you can easily go negative but rank up fast). TDM kills for each Prestige are around 2500, slightly less or more depending on how much "teamwork" you do with regards to assists, assisting streaks, enemy streak destruction, etc.
This puts Prestige Master at 27500 kills via TDM, I would imagine 30000-37500 for other game modes.
I'm a Prestige Master. I usually play Hardpoint, Domination, Headquarters, or Kill Confirmed.
My stats are:
6 Days, 20 Hours, 1 Minutes, 19 Seconds
It took me around 9 online days with 29K kills and SPM was 280. I've seen people get there around 5 online days, but that requires a high SPM and good W/L because the XP you get as a match bonus is high, or maybe it's also possible with a low W/L if you killwhore enough in objective modes.
I played on both dxp weekends but not as much as i could've, and maybe 50% of total time played was on TDM where you do rank up slower. I also played a lot of HC FFA while racking up OHK's for the semiauto and burst shottie, maybe 1 online days worth, so that made the progress a lot slower too. Sticking to full auto weapons will also get you there faster in my opinion, as you are better off overall with them, i died a lot when i was getting diamond camo for my shotties (excl. using the Remington) and some while getting diamond on launchers.
Doing well in KC and Hardpoint will get you there faster, or playing in the chaos moshpit. For example my SPM in TDM is around 220 and around 350 in Hardpoint, while that is not the same as XP they do have correlation between them obviously.
Having no lag issues would help a lot too because then you don't get those BS deaths like i do in nearly every match i play, which means more deaths and less XP, and more losses. My stats took a huge dive after launch week when the lag issues started for me, and stayed at that lower level because i continue to play a lot. Post patch 1.03 my KD went from 2,1->1,4, WL 1,5->1, and SPM from 350->280, these are rough estimates as i cannot remember them accurately, but factor those in and obviously ranking up becomes slower.
it took me about 7 days. i didnt play during the recent double xp because i already reach master prestige. my spm is about 400-410.. about 30-33k kills when i reached master prestige. and was ranked 482 at that time..