Hello,
I would 4 bet around 2.5 times the size of the 3 bet preflop.
2.2 times is too cheap to me (I am not sure I am right as you have position on him)
I don't see the point to shove flop as it is not a drawy flop to me. I am not too scared of flush in a 3 bet pot and I wish to keep him and i don't want to make him fold worst hands.
However his sizing Flop is quiet annoying, I would raise around 20bb I think there, to make it as around half pot and shove on any turn if it is not an ace on the turn.

I don't know your opening range UTG preflop, and profile of your opponent, but personally I don't three bet often TT and JJ from SB versus UTG, cause the range of villain should be tight, then you expect quiet a lot of call or 4 bet, and you won't be in position to play well the pot.
To me you are facing mainly QQ++ and AK on this spot.

IP you can use variety of sizing's for 4bets: from 2.2 to 2.5 depending on 1)ranges 2)positions 3)how deep you are 4)opponents

However here I think you give him too good odds to call, partly because original 3bet was quite small and he can continue vs your 4bet pretty wide(i'm sure all PP he 3bet should be peeled vs 4bet along with AJs+)

Flop I like raising. He can donk this board sometimes but our response is to raise a lot vulnerable hands otherwise his line is too good with something like 88-TT . You don't have to jam tho put around 4x raise and shove turn