His argument is not flawed and his experiment and description of it are correct. This topic has come up a couple of times before, so you can do a search and dig up more information.
The only issue I see is one of semantics. The good Professor clearly defines what he means by Kirchoff's Law, and specifically he defines it as the statement that the integral of the electric field around a closed path is equal to zero. If you accept this definition, then that's the end of the story - he is 100 % correct. However, there are at least two competing definitions of Kirchoff's Law in text books. Many books define Kirchoff's Voltage law as the statement that the sum of voltage drops around a loop is equal to the sum of EMFs around a loop. If you use this definition, you can let it conform to Faraday's law, and all is well.
Personally, I hate arguing about semantics, so I won't detract from the thread with any claims that one definition is better than another. The last time we talked about this, I decided to go to the library and do a survey of books, both old and new, I was surprised to see that these competing definitions exist in physics and electrical engineering books throughout the 20'th century.
Personally, as an electrical engineer, I prefer to carry around a version of KVL that is consistent with Faraday's Law. False laws don't really help me very much - not in theoretical work, nor in practical endeavors. They do make for very provocative and exciting lectures though.