With cisco devices the logging synchronous command will stop logging output from interrupting the the CLI session. Is there an equivalent command for the fortigate firewalls? i.e. When running a debug on the firewall is it possible to keep the cli prompt below of the debug output at all times so that typing/input is never interrupted?
No, this is not possible in FOS. Even with multiple (ssh) terminal windows, debug info will be printed on ALL windows. Multiple terminals will only faciliate command input.