Hi, I am also having this problem. It is very intermittent, some days my ADS would flicker to the point that I can't even ADS at all and some days I have no problem with ADS. I am using a SteelSeries Rival 310 with the Steel Series Engine 3 software. It is definitely NOT the mouse as I have tested all the buttons with a mouse clicking tester online. I have also repaired my game files and it still hasn't resolved the problem. I am currently uninstalling and re-installing both Origin and Apex Legends as I'm typing this, hopefully it'll band aid the issue before a real fix can be made. Today it's happening so severe that I can't actually play the game.
UPDATE: Uninstalling and reinstalling Origin and Apex Legends does NOT fix the issue.
UPDATE 2: Disabling GeForce Experience, Origin In-game Overlay, MSI Afterburner & RTSS Overlay, SteelSeries Engine 3 does NOT fix the issue.
NOTE: The severity seems to be dependent on the servers. For example, It seems to happen more severely in New York and not Iowa servers. FALSE
NOTE 2: This happens with both Toggle and Hold ADS and highly unlikely to be a hardware issue.