-k flag in older
modprobe versions was used to set the
autoclean flag on loaded modules. The autoclean flag was part of a mechanism in the kernel that allowed loaded modules that had not been used for a while to be unloaded automatically. If you listed loaded kernel modules on such a system, you could easily tell which modules were loaded with the autoclean bit set by looking for the
(autoclean) tag somewhere on the line for the listed module.
-k flag is missing from recent
modprobe versions. I cannot say with certainty whether the use of this feature has been depreciated in recent kernel.
You could look at the manpage for an older version of modprobe here. And this, and this mention the autoclean flag.