Do you mind expanding on this and showing a full flow? That sounds a little wonky to me but I could be missing something.

Our flow is like this:

1) Person pushes to dev branch

2) Chat log shows the feature pushed

3) Chat log shows Jenkins received push and is downloading

4) Chat log shows whether tests were successful (yay) or not (boo).

^^ that's the basis. It helps keep everyone up to speed on what's going on, especially for testing.

One more example: Notifications when merge requests are made / merged in the chat.