Some locals/installs 12' will work just fine, other places it won't. I'm a strong proponent of good draft, I had bad draft and don't wish that experience on even my enemies. You can't keep your glass clean, really hard to get your fire started, reloading causes tons of smoke to pour into the living space (and often set the whole house smoke detectors off), the spilled smoke made the place dirty, and I couldn't even think about lighting a fire if it was warmer than 45F outside. I had a number or problems, a short chimney, the chimney wasn't enclosed in the attic space which made my inside chimney part of the outside envelope, an overly ovalized flex pipe going through the damper, and mis-branded connection pieces caused gaps in my liner. I ended up ripping out my entire install, enclosing the attic space around my chimney with metal, cut my damper so I didn't have to ovalize, purchased a new round flex pipe, removed the mis-branded connectors, and purchased an extend-a-flue to increase my chimney height 4'. It's such a joy to use now, and no more dirty glass (except the extreme edges) or smoke spilling into the living area.
I believe 15' is mentioned in most as it pretty much covers most situations. Here's what I learned about draft so I could figure out what I could do to improve mine. The chimney height helps draft, the more surface area the more it sucks your draft. A short chimney doesn't have a lot of surface area so it doesn't have as powerful a draft.
Since draft is determined by temperature differences between inside & outside, the warmer it is outside the more powerful your draft needs to be to overcome it. That's to say a short chimney since it has less power will have more problems trying to have a fire going when it's warmer outside vs. a longer one. You'll probably experience this after you get your insert installed you'll want to light it off and see how it does when it's 65F outside and find it difficult, maybe impossible and your glass dirties up. There's a certain temperature outside you'll eventually find where you simply can't get draft. I've lit a fire in my insert at 58F outside since I redid my install and was able to do it, it was previously impossible unless 45F or less outside.
Inside chimneys draft better than outside (in part they're already warm, and outside chimneys can be reverse drafting when not in use).
Outside environmental influences play. I live in New England, and find those cold foggy thick days it's hard to get a draft going, like there's heavy air above your house that won't let smoke through. I can tell those days when I start a fire and the smoke comes out my chimney then spreads horizontally unable to penetrate this "barrier" above my house. The smoke sort of makes a cloud above my, and my neighbors houses instead of flying up and away (until secondary burn gets going). Those days it takes a bit more babysitting. On real bad days the smoke comes out my chimney and falls to the ground. Once secondary burn gets going, there is no more smoke so you don't see it anymore.
Flex pipe restricts draft more than rigid, Insulated pipe heats up hotter than non-insulated giving stronger draft, bends interfere with draft so the longer your straight run the more draft you'll have.
Case in point, a 12' insulated, internal chimney, straight run, rigid pipe, not ovalized will draft better than a 15' flex run, with a couple bends, ovalized, on a exterior. Also, I believe the closer you are to sea level the better your draft. Those in Colorado as I understand should err on longer runs.
So, you may not need 15' but will find your experience and enjoyment better. That part that sticks out of your chimney if longer than 4" or so needs to be insulated else it'll hinder your draft more than help. If not insulated it'll rapidly cool the exhaust down causing creosote to form and slowing down the exhaust at the end, causes a slowdown in the whole system. To extend my chimney I continued the single-wall stainless 4' out of my chimney, did the storm collar & sealing, then insulated the part sticking above with kaowool, and protected the whole thing from the elements with an extend-a-flue.