Yep Stress Coat is a water conditioner as well so you don't have to use the Betta Bowl Plus. I don't want to say all water conditioner's are created equal but they will all do your base things like getting rid of chlorine and usually heavy metals in the water. But the better ones like Prime, Stress Coat and API Tap Water Conditioner get rid of more than just those two things so I'd suggest looking into them as well. But you'll only have to use one at a time unless your tap water has ammonia in it; then you should be using Prime all the time.
You can use some in conjunction as well like if you did have ammonia in your tap so you'd have to use Prime at all times but then if your Betta ripped his fins, then you can use Stress Coat on top of it. Of course I don't suggest it all the time, it won't hurt him but it's just basically over kill and not needed at all.