Oh my, I think that *industrial* space standards for BB White turkeys are like 3-5 sq ft per turkey, right? (And that is with them only getting to 15-30 lbs live weight, not growing 'em up giant like some do at home). AND, that is with a large area, so that they actually have more room to move around.
IMHO, if they have an *ample* run or are free-range, then 4x6 is BARELY adequate for nighttime quarters for 3 BBWhite or BBBronzes. (Having done that myself last summer). If you have heritage breeds that don't get as large and the turkeys are young, you might put another one or two in there.
Really, though, even just for nighttime quarters, I don't think you'd want any less than 8x6 for six turkeys of whatever description, and if their run is rather unappealing (soupy mud, or on the upwind side of the building, or if you're going to keep them over winter in a cold-winter or nasty-storm-prone area) then I'd suggest at least doubling that.
My current heritage bronze pair has 8x6' indoors, and while it is comfortably adequate while they are going out all day right now, because I will not be able to do that for some parts of the winter (for various reasons not related to turkey hardiness) I am going to have to figure out how to section off another part of the indoors of the building so they can have more area then.
Good luck, have fun,
Pat