Instagram, like any self-respecting social network, has its own integrated chat feature. How do you know who you can chat with, though? The mystery will be solved as soon as the latest feature rolls out: online indicators. It's revolutionary.
You'll have to pardon the iOS screenshots, but the feature should look the same on Android. When one of your friends is online, they will have a small green dot on their avatar in the direct messaging list. If you see that, you know they're online and available to chat. Instagram will also offer status messages like "Active x minutes ago" and "Typing..."
If you don't want people to know when you're wasting time on Instagram, you can head into the app settings and disable your activity status indicator. You might end up regretting that if you use Instagram to connect with friends, though. As online status becomes ingrained in the experience, people might just stop messaging you because they think you're never online.