I believe this claim is true.
An article from CookingLight.com says that "It's because of a type of sugar called raffinose that's found in asparagus, Brussels sprouts, broccoli, radishes, celery, carrots, and cabbage. These veggies are also rich in soluble fiber, which doesn't break down until reaching the small intestine and can also cause gas."
CookingLight
According to an article from the National Library of Medicine, "RFOs (raffinose) are indigestible and cause flatulence in humans. Expulsion of these gases causes severe abdominal discomfort such as abdominal rumblings, cramps, diarrhea, and nausea." Radishes contain a sugar called raffinose that causes symptoms of passing gas.
National Library of Medicine
According to MedlinePlus, "Soluble fiber attracts water and turns to gel during digestion. This slows digestion. Soluble fiber is found in oat bran, barley, nuts, seeds, beans, lentils, peas, and some fruits and vegetables."
MedlinePlus
An article from MedicalNewsToday lists symptoms that may accompany with eating fiber which radishes have, "bloating, gas, feeling too full, stomach cramps, constipation or diarrhea, etc."
MedicalNewsToday
Therefore this claim is true as radishes contain both soluble fiber and a sugar called raffinose that both cause bloating, and increased production of gas. Eating high amounts of radish will cause these symptoms to become more prominent.