In the english language, a "red herring" is something that misleads or distracts from a relevant or important question. I would like to know if there is an equivalent phrase in Japanese.
I haven't known the word "Red herring"!! And I confirmed the article below.
It's not originally from Japanese so this may not be the answer for you, but we commonly use "ミスリード" as the loan word of 'mislead'. In most cases I think we can use that.
Common Red Herring Examples: Example 2 (Eden example)
Common example 2 in the above article (about Eden) sounds exactly "ミスリード". And it's also like "論点のすり替え" as Sadaharu-san explained.
Literature Examples: Example #1: Da Vinci Code
Literature Examples: Example #2: Sherlock Holmes: Hound of the Baskervilles
In the literature examples, we may call it "ミスリード" too. But it doesn't sound common maybe because we use "ミスリード" for telling negative thought. Rather we use "伏線"('foreshadowing') for such cases. Many Japanese like this word because it makes stories exciting, so it's very popular word in Japan. However, "伏線" mostly doesn't lead to false conclusion. Regardless of leading false conclusion, we call such techniques in a literature "伏線".
However, the next one is far example from "ミスリード".
Common Red Herring Examples: Example 1 (Conversation with a child)
Interesting!! I often see such a conversation but I don't have any exact word to describe this situation in Japanese!!
The "red herring" is famous for the titles of movies. But I haven't seen any of them. I do not know what is the exact equivalent but I try to bring some.
論点のすり替え - Ignoratio elenchi, is a popular way of answering/asking a little out of topics and get far away from the original topic.
世論/意識誘導 - is the same as the leading question, instead of using questions, use commercials and headlines to hide something from what mod doesn't want to let them know. Public opinion manipulation.
隠蔽工作 - is the direct name of 'cover-up'.