As a Chicago resident so do I. Just listen for the screams and shot reverberation off the nearby buildings. It doesn't take much practice to hone it down within 50yards or so. Don't need no app.
I've been to Chicago once (visiting a family member), it's absolutely crazy. I could never even imagine living like that. Never before in my life have I been genuinely scared that if I left the house at night, I wouldn't come back alive.
I've also been to Chicago once (going to an Anime con up there; was a meet up for AMV creators worldwide, and while I wasn't one my brother was), but it was a chill and nice experience for me. The last time I heard gunshots was actually this past new years, when my neighbor fired off like 12-15 shots during fireworks (GA, not in Atlanta but not too far either).
It's pretty normal during the day, but at night, once you hear gunshots a few blocks away, I would really avoid going out. I've never seen something like this before.
Statistically no, it's not very dangerous as far as big cities go. Its homicide rate is ranked 30-something in the USA. Pretty much every city has "bad areas", though.
Not an app, but here in Germany we have a public warning system that broadcasts an alert to all phones in an area in case of catastrophic events. Happened twice in my city since I moved here two years ago. Once for a mass shooting, and once for an accident at a chemical plant.