In the past i remember the spurs using a starting line up featuring Duncan (no floor spreading), Splitter (no floor spreading), and parker. (rarely shoots threes)
Then they have danny green and leonard who both shoot a good amount of threes. Maybe burks shooting 2-3 per game is enough if hayward and trey shoot close to as many as green and leonard (since burks already shoots about twice as many as parker, hayward and trey would not have to shoot as many as green and leonard even)
The heat won a title with a starting lineup of Jason williams, d-wade, antoine walker, haslem, and shaq. Only two volume three point shooters.
Maybe the lack of three point shooting for the jazz is more of a team problem than a single player problem. Maybe burks, hayward, and trey all need to take more threes since it seems that you can win titles with only 2 volume 3 point shooters in the starting lineup. We dont really have any volume three point shooters in our starting lineup (is hayward or trey a volume 3 point shooter?) so maybe all three of them need to take more.