The first thing I would check is the FD cage alignment and height.
Fixing that might solve the problem.

The next thing I'd check is the chainline.

Also, to avoid misunderstanding:
Does the large front ring combined with smallest two rear chainrings (the ones most outward, away from the bike) cause rubbing?
Because, if it's the largest front ring with the largest two rear chainrings (the "slowest" gears, closest to the frame), then we're probably dealing with cross-chaining and some chain rub might be inevitable, depending on your chainstay length (which is ridiculously short on most modern bikes).

Relja