Some common Providence melee combos i tend to see are:
cc8b>8b->BR
The BR is usually there, but if their partner is really trying hard to cut you I think you can forgo the BR and dodge
(when in burst):
cc8b>8b>8b>8b
or
8b>8b>8b>8b (both of these do ridiculous damage)
cc8b/8b>8b>8b>super also works
Not only are those consecutive kicks hilarious, they're also incredibly strong. Note that the rainbow steps after the 8b must be forward for the rest of the kick to connect.
If you get desperate as well, bb>bbb works okay for me in close quarters situations (providence melee is surprisingly fast)
But yeah generally in melee situations try and resort to using 5ac and boost/stepping away while shooting 9 beam rifles into their face
A thing with 5ac as well is if you down your opponent, you can pop 5ac, run up to them and wait for them to wake up. When they do wake up, fire the 5ac (you want to fire a bit before they come out of yellow lock). You also can't stand still, you need to try and move in circles around them while they get up (meaning it also takes a bit of luck for this to work.) If it works successfully, you'll catch them waking up with your 5ac and knock them back down. It's fairly consistent I'd say, but it is a bit of luck.
And a lot like other moves in the game, 2bc won't change the camera when you send out the three dragoons (very useful, camera changes suck)