As far as I know, Rod Serling’s widow, Carol Serling, still holds the copyright to her late husband’s work. I have no idea how aggressive her legal resources might be, but given the pioneering role of The Twilight Zone in TV history, I would advise great caution in appropriating anything from the series without full attribution and preferably permission.
If you do find an episode that is based on something other than an original script by the series host or one of the other writers who worked with him, then I would say the question goes back to the source of the idea and not to the TZ script. The TZ episode, of course, would still be a proprietary realization of the concept. Serling was such a font of ideas that I find it hard to think he copied from anything, other than to make use (as all authors do) of themes and motifs present in the culture, such as space exploration, racism, nuclear holocaust, etc. That is not what “copying” means. Most serious authors have immense respect for the rights of authorship of others.
I would not think it was a good idea to demonstrate your skills in a medium beginning by violating the fundamental concept of an artist’s rights in his own material. I would want to show extreme respect for the best work of others in my field and also showcase my own originality.