I analyzed about 370k ranked solo queue games played on Patch 5.6 and found about 600k unique players. Here's the frequency table for these players:
|Flash on D||Flash on F||Not Identifiable|
|# of Players||301269||290322||10947|
In summary, there are slightly more players who use D for Flash than F. Note that the "not identifiable" 1.8% of the players are due to a combination of inconsistent use of D and F for Flash and/or running no Flash at all.
More interestingly, it is possible that players who use D for Flash have slightly different lane of preference compared to players who use F for Flash - although the difference in preference is fairly small. As you can see below, players with Flash on D chooses to play mid lane 19.8% of the time; for players with Flash on F, it's 20.5%.
|Player \ Chance to play||BOTTOM||JUNGLE||MIDDLE||TOP|
|Players with Flash on D||40.2%||20.6%||19.8%||19.5%|
|Players with Flash on F||40.0%||19.8%||20.5%||19.6%|
Again, the difference is small, but a chi-squared test of independence shows that the difference is significant so the choice of D or F for Flash and choice of lane are probably not independent.
I have a theory for the result above.
First of all, why do some players choose D and some players do F for Flash? Well, when you play your first game on a level 1 account, the game places Heal on D and Ghost on F by default. Flash is not available for a level 1 account; but over time you will gain the option to use Flash and you will be faced with the dilemma of assigning it to D or F.
I think at this point, the decision to use D or F for Flash depends on if the player thinks Flash is similar to Ghost or not. If the player treats Flash like a movement spell similar to Ghost, I think it is natural to keep Flash on F. On the other hand, if the player treats Flash differently from Ghost, it makes more sense to bind it on a different button.
Therefore, the choice of using D or F for Flash may be demonstrating different modes of thinking for players - and perhaps the button choice is a reflection of the player's personality. Because of this, we also see that players who choose D for Flash have slightly different lane choices compared to players who choose F for Flash.
Then again, this is just my theory. It would be cool to be able to do some personality tests on players and see how personality correlates with lane choices though!
 Feel free to rip me apart on how I inappropriately used chi-squared test here.