What's the correct phrase to use? In our app or on our app

Both of these phrases work for the intended purpose. "On our app" is probably the more common phraseology, and sounds a bit less clunky, though the message would not be impacted either way by the use of either of the phrases. The distinction here is nonexistent, and in other places so subtle that many languages (such as Spanish) don't even have separate words for the expressions.