Turn off the target app's Setting
In the case of facebook Messenger


1.Tap the icon at the top left of the screen to open your settings screen.

2.Tap the Notifications & Sounds

3.Turn ON the check Notification previews

4.Tap the Manage notifications
 
Set each channels as follows.
 Change Sound to "None".
 Turn OFF the check Vibrate
 Turn OFF the check Blink light
 


The notification sound continues to be heard while Messenger is running.

If the "Chat heads" function is ON, this app will sound all the time in response to the chat head notification.
In such a case, create one keyword setting, specify "Chat heads active" for the keyword, and then specify "Do nothing" for "Behavior for notification".
That way, chat head notifications are ignored.