Is there any way to enable/disable it using the CHDK menu? Or is it activated by CHDK and camera type automatically?
Neither option is available.
Precision sync is currently something that must be built-in to CHDK at compile time using an option in the platform_camera.h file (CAM_REMOTE_USES_PRECISION_SYNC) . So far this has only been done for the A1200 - mostly as a "proof of concept". I believe the intention was to enable other cameras "on request" if the standard sync code was inadequate and if the requestor was willing to test that it worked properly on the camera.
Is there any solution available for the precision sync together with flash? (I remember there was an issue)
AFAIK, there have been no problems reported in the CHDK forum about this.
SDM users may have discovered issues but if so, they have not shared the issue and SDM source code is still not available (after more than two years of freely distributing GPL based SDM 1.86) so I cannot confirm this.
Regardless, there has been no work on this possible issue for CHDK ports.