I've heard those rumors too and to be honest, that seems like a plausible theory. But there are 2 counteracting facts for that theory. The first is that Jiraiya's body was lost into the ocean when pain destroyed his back with chakra rods; so its almost impossible for anyone to have acquired his DNA, except maybe they got it long before he died (or how Kabuto wanted to get his DNA).
The second fact is the way Kashin Koji's personality is displayed in the manga, unlike Jiraiya, If i were to describe his personality, Kashin Koji seems more like a self centered, "no nonsense" type of person who is serious minded and very calculating. That is very contrasting to the fun loving, super pervy and social Jiraiya that we all know.
Also, It seems very unlikely that Jiraiya had a son, but then again, since Jiraiya was such a perv, it wont come as a surprise that the one and only ERO SENIN had some secret relationship and something along the lines resulted in Kashin being born.
Nevertheless, the theory that i feel could be the closest is that Kashin Koji could be a student of Jiraiya Sensei. Since Jiraiya was able to teach Naruto the rasengan and summoning jutsu, it would make sense to hypothesize that he probably taught other students too. The possibility that ERO SENIN had a couple more students aside Mnato, Nagato and his crew, and Naruto is not a far fetched idea. Lets not forget that after Jiraiya recieved the Great Gamamaru's vision of the future, he decided to go around, traveling and looking for the so called "child of prophecy". He might have had a couple other students during the years that he travelled around writing books.
PS: My answers are based of assumptions so there's a possibility that I could be really close, or completely wrong in the theory.