I tune all my basses to D standard now, and mostly flats for me, too. I do have a set of TI Jazz flats on a fretless, and they are kind loose, but then I think they work for that bass (used to have light-gauge rounds on it tuned to E for years, don't think there's much difference in tension between the two).
But for "real" flatwounds, I have to say my favourites would be GHS Precision flats, the set with the .055 G string. (I guess that would be the F string for us.)
Rotosound flats are higher tension for comparable gauge, and I was not terribly fond of them until I tried them on my Roadstar. It's like they were made for each other.
Also have a set of LaBella "Jamerson" flats I am going to try on my Musician (currrently with the GHS flats), but I can't comment yet. They should certainly have enough tension even at D.
There's also the Ernie Ball Flats, they make a set with a .110 E string. (I've been meaning to try that with the A, D and G strings from the GHS set.)
And Webstrings Detroit flats? They also have a set from .110.
I guess the bottom line is, you shouldn't have any trouble finding a set of flats with more than enough tension tuned down to D.
Oh... I've also tried the regular LaBella Deep Talkin' flats and Sadowsky Black Label flats (both the heaviest gauges), and found them to have more than enough tension, just not the sound I was looking for at the time.
Good luck.
-Alex