I got in that store yesterday, so, I can help out here - Basically, you'll have to coordinate your style with the clothing styles shown on various racks att Boutiques stores Kalos. For example, if you see, say, a blue blouse, blue shorts, white socks, and cyan mary janes, with a orange bag and blue hat with silver accessory on display, then, you should be wearing those for them to let you in.
Once you do get in, you'll see that their prices can be.. a little high - as little as 80,000 - 10,000 yen.
It's given to you from a girl in the Coumarine Hotel if you show her a pokemon that is quite friendly to you.