When it comes to accuracy, it's not so much flat base vs boattail as it is compact vs long and skinny. Short, stubby bullets don't require as much spin and are more tolerant of defects and less than perfect launch dynamics. This makes for good accuracy. It also makes for lousy ballistics, which is why the long skinny boattail bullets dominate long range - they pay the price in accuracy for better wind resistance.
The why's of this are complicated, but I stole some wisdom from Bob McCoy and took a stab at writing it up here:
https://bisonballistics.com/articles/jump-sensitivity-factor-a-new-old-way-to-evaluate-bullets
It turns out you can calculate a number akin to a BC, but for accuracy potential. I call it Jump Sensitivity Factor (JSF), since I can't find a well used name anywhere else, but the lower the better. A typical long range bullet might be in the .150-.200 range. A short range bullet should be around 0.060. The best bullet I've run the numbers on so far is a 112gr BIB .308 bullet, which came in at .046! What's good for JSF is bad for BC. That's why there's always a trade off when designing bullets.
I have tested this math by varying the amount of lead in the core of a bullet, and calculating the JSF for the different weights. The math predicts groups will shrink as cores get lighter (to a point - but you run into structural problems before a bullet gets "too light"). So far, my test results have agreed with the math very well for my bullets.
When you crunch these numbers, it turns out that a short boattail isn't all that different than a flat base if you're talking about light bullets, assuming all else equal. It's a relatively minor effect.
Granted, this is just the effect of the boattail on the bullet dynamics. There is obviously more to accuracy that isn't so easily understood (by me at least). But this is a big part of it.