The polite form is to say he is repeating the year. For example, "Peter is repeating Grade 4".
"Flunked" is too strong a word as it is very critical. You would never use it for a young student. For someone older, you could use it but it is derogatory so you'd only use it as an insult, joke, or to mock the person.
So "Repeating" is the best word word to use, as it is suitable for any age student - primary school through to university.
"He repeated year 3 at school"
"She's repeating her year at university"