Horizontal flute racks are a nice aesthetic, but vertical is very practical (and not unattractive).
Greetings!
I just happen to know a "craftswoman" gal that makes some pretty cool flute stands that are totally vertical. You can ask Jeff how he liked using the "Stage Tote Ten" flute stand that he borrowed to use on the stage this year at Musical Echoes!
Perhaps you can take a quick trip to EBAY and enter Native American Flute Stand and check out the stand listed as; Turq Inlay Flute Stand for NINE Native American Flutes
There are actually several fine folks creating a nice variety of flute stands are racks, and it is truly terrific that we all have many options available to us.
It's sort of funny, but what started out as a simple need for a flute stand, has turned into quite a busy little cottage industry. Yes, that's me; Standing Flutes! I'm amongst the ranks of many crafty folks who seem to always have saw dust stuck to all our socks!
I readily discovered that my hand crafted vertical flute stands are quite handy, practical, and greatly appreciated for a number of reasons.
Yes, your flutes seem to dry out just fine being stored vertical, but like many others, if I have played one particular flute for a lengthy period of time, I take off the bird and allow the flute to dry after I have done the serious "death grip hold and swing" method to expel any excess moisture out of my flutes. I often warn people to hang on to that pup for dear life since none of us ever wish to let lose of a flute in mid swing!
Otherwise, right off the bat I started placing felt pads at the bottom of the dowels to catch and excess moisture, and to further protect the ends of the flutes.
Yes, you can store many flutes in a minimal amount of vertical space as long as the flutes are spaced properly so that they have ample room to spread their wings, so to speak!

I will readily admit that I also have one wall rack that was gifted to me, but I am limited on wall space and the vertical stands seem to work best for the rest of my flute babes!
Since I do not have all of the tools necessary to make wall racks, I leave that up to other wood working folks like Jim Adams, of Cedar Song Flutes who makes a very handsome flute wall rack.
I know many folks who use both types of stands/racks, and their choice is often dictated by the amount of space they have available in their home or office.
I have received numerous emails from some folks who tell me that they fear for their flutes when they are perched on a single horizontal table top flute stand, but perhaps those type of stands/racks are located in a precarious spot to begin with, or maybe they are placed someplace where children or pets can bump into their flute and cause a potential disaster. Whatever is the safest resting and drying spot for a flute, is what should work best to protect your flutes.
For those folks who truly have a hefty and quite valuable "Flute Fever" collection, flute safety is a generally their number one priority for sure!
When you see photos of how Dr Richard Payne stored/displayed his flutes, it is totally amazing!!! But then again, there will not be many flute collectors in this world with such a vast collection.
By the way! The flute gunk someone else mentioned could actually be somewhat of a health hazard. It may greatly benefit you and your flutes to periodically remove the birds/blocks and make sure that your flutes are indeed free of any mold growth. Here is North Florida, like many other places, the humidity can do a nasty number on your flutes if they are stored wet! If your shower curtains or shower walls have a tendency to mold, then you can pretty much expect a wet flute to do the same thing. I recently attended a Pulmonary Symposium, and one of the health topics was "sick building syndrome". Your flute is indeed a house of sorts, and it should be cleaned periodically, or on a routine basis to prevent any possible harm.
Dust bunnies can cause problems too!

I am, by no means an "expert" on any particular subject, I just happen to know a few things that are quite beneficial when it comes to enjoying the overall fluting experience! If I am wrong, then please steer me in the proper direction!
Experience is indeed a dandy teacher and I thank all of you for sharing your flute experiences!
Cheers to all the flute makers and flute fanatics, Marsha