Interestingly an armor jacket has an availability rating of 2, as does armored clothes – while an armored vest has a rating of 4. Apparently it is easier to go out and buy an armored jacket than it is a vest, and do note that there is no restricted tag on that availability, so it is legal. As noted, private property may have its own rules.
Some armor jackets are no doubt designed to look like armor, be imposing, etc. If you are security or a ganger you want to communicate that you are geared and tough. But that doesn’t mean that some aren’t cut in less obvious ways. It is still going to be a jacket of some weight, probably with a collar that can provides some neck protection when worn properly, so nobody is going to mistake one for a sweater or suit jacket or something. But I would think that they could pass for a bomber jacket or ski jacket or pea coat with built in neck flap, etc. (why do I say it has neck protection? Well, a vest plus two armored sleeves (from R&G) gives armor 11. A jacket might be a bit heavier, but I figure it also provides a bit more armor coverage—probably further down the hips and more coverage around the collar bones and lowest point of the neck).
Sure, a careful observer may be able to spot differences in how it hangs and moves, but that is why things have a concealability rating. And there are plenty of places where wearing a jacket like that may be conspicuous. But I think it is overkill to say that wearing an armored jacket into an arcology is going to get you promptly tazed.