I guess it really is going to depend on what they mean by “vintage”. Looking at their website, it seems like they mean anachronistic circus looks, vaguely turn-of-the-century. Corsets, louis heels, feathers, fringe, top hats and bowlers, Moulin Rouge, that kind of thing. “Steampunk in colors other than brown” seems like a good byword for this outfit, meaning don’t get hung up on period accuracy because this is circus/entertainment, and not a reenactment. The performers and employees on their site are wearing clothing mashups across the 18th, 19th and 20th centuries.
I would look at the work of Toulouse Latrec for inspiration, because the venue is definitely trading heavily on the Moulin Rouge look, which he coined. I included a ton of his work above, but there’s even more if you want to google.
Some touchstones to make these outfits suit the “type”: black or white gloves, black or white or solid-colored opaque stockings, red lips, dainty boots, gibson girl hair, hats, monocles, jewel tones on black.
I’m not sure if you’re looking for male or female wardrobe, but imo it is easier to put together a more typical women’s ensemble in this style.
Men’s clothing involves fewer layers and drapes, and is usually very strongly dependent on the cut of the garment to sell the period style. But there are some nerd tricks that can work sometimes. You can do a lot with a basic white buttonup and a small scrap of fabric:
Sleeve garters are another outfit cue that says “vintage” and can help sell a regular Kmart buttondown.
Sashes are a good alternative to a cummerbund for a circus look. It might make you look a little like a halloween pirate or a vampire LARPer, but that’s actually not necessarily a bad thing in the context of what I’m seeing on the Spiegeltent site. You can make the garters out of old bra straps or underpants elastic. Covering them with fabric is an added step that can help disguise the source. If you don’t want to sew, safety pins will hold it all together but make sure they are not visible, and make sure they are strong and redundant so you don’t get stabbed during your shift.
If you have a vest, great, just make sure it’s TIGHT. Baggy or boxy vests are the #1 fuckup on anachronistic men’s outifts; baggy vest says “prom” or “dad’s suit” louder than almost anything else except maybe a badly-fitted jacket. if your vest isn’t form fitting, take it in at the sides with sewing or concealed pins, or cinch it in the back. Clip elastics are a good option here:
Search for “dress cinch” or “elastic dress clip”. They can often be found at craft stores and are insanely useful for all kinds of clothing issues.
Ladies’ clothes are a little easier imo. If you have a corset or anything that looks vaguely like a corset you can drape your entire outfit around it and use it to hide the safety pins holding the whole thing together. For example, you can fake a bustle skirt like this:
Make sure to experiment about where the best place is to pin. This method will work with any length of skirt, but I find the witchy/hippie “broom” skirts you see in farmer’s markets and thrift stores, with as much fabric as possible, work best. Make sure your bustle is symmetrical, with the drapes the same size on both sides. Depending on where you pin, the front hem of your skirt may dip lower than the back. This is a matter of preference. Here’s another bustle method that makes a central drape, instead of two.
You can wear this by itself, or on top of another skirt of the same or different color, or with a petticoat, or even on top of another fake bustle.
You also don’t have to use a skirt, pieces of fabric work fine. If you’re using a bedsheet—and I have—make sure you’re concealing the telltale hems, which is how people will be able to tell! Hide your safety pins and elastic and bunchy edges under a vest or corset or sash. Corsets are really great for tucking things into because they will flatten out bulges caused by hidden fabric and folds.
I really like this fake bustle method and I use it all the time because it is no-sew, and you can build dozens of different dresses out of a single skirt and some safety pins, and just tear it down at the end of the night.
Footwear is pretty important too, but not everyone has access to retro shoes and that’s ok. Men’s shoes are the biggest difficultly here; women’s shoes can be concealed a bit. One thing you can do is tie a long ribbon under the arch of the shoe and around your ankle, creating a circusy, ballet sort of look.
As a bonus, this really helps your heels from popping out the backs of your shoes and can prevent blisters during a shift. The ribbon will migrate around a bit as you move, unless you pin it down.
A couple last words of advice: Polyester or rayon satin, cheap crushed velvet, and cheap scratchy lace almost always look tacky, like a premade halloween costume. Satin also wrinkles instantly and gets runs easily. It’s better to avoid these fabrics if possible, even if it means sticking with cotton. If you’re wearing a bra, keep it concealed. Modern underwear is a big jarring “tell” that can hijack “vintage” looks. Opaque jewel tone, black or white tights are very Victorian-looking, and if you want to go whole hog you can cut them off at the tops of the thighs and tie them above the knee with ribbon or elastic. Feathers and fake flowers are a lot cheaper at the craft store than they are when already sewn onto headbands or hats on Etsy. Cat toys maybe be an even cheaper source of feathers. When you’re in a fabric store, ask where the “remnants” rack is and make a beeline there. Chances are you aren’t going to need more than a couple yards of fabric or ribbon, so why pay for pristine yardage from the roll? Interior designer fabric sample catalogs are often discarded whole and you get a huge book of foot-squared, extremely expensive and durable sofa or curtain fabrics. You can also find cheap fabric in the form of curtains, sheets and large size clothing in thrift stores. Furniture trim, like little pompoms or tassels or beads, are durable as hell and it doesn’t take much to edge a hat or a corset for a night. Tie a long thick sash into a big fat bow and put it on top of your fake bustle; it’ll look great and hide your pins and edges. If you’re wearing jewelry, try to make it all one tone or metal (gold or copper or silver), OR make sure the mix is fairly even.
I could go on but this has been a few hours already. I hope this helped, and break a leg on your application!