A flaming dodgeball is a metallic flaming dodgeball made of Celestial Bronze. They explode on impact.
The Laistrygonian giants threw flaming dodgeballs at the Meriwether College Prep students in the school gym. Percy Jackson and Tyson had to dodge the "dodgeballs" as they were being thrown. Percy was unable to attack the Lastrygonian giants because he didn't have Riptide (his magical celestial bronze sword) with him at the time. Where Riptide would normally return to his pocket, Percy's gym shorts didn't have pockets; therefore, he didn't have any way to carry Riptide around. Tyson was able to catch the flaming "dodgeballs" and throw them back at the Laistrygonian giants, because he is a Cyclops and is immune to fire. Percy described them as perforated like wiffle balls, with fire bubbling out of the holes. When hit with the flaming dodgeballs, the walls were blown apart. Although the balls were made of Celestial Bronze, they still hurt mortals, but didn't severely damage them as they would a demigod.
When Percy, Hazel Levesque, Frank Zhang and Ella arrive at Frank's house at night, Laistrgonians are camped out along the property line. In the morning the Laistrgonians hurl flaming "dodgeballs" at the mansion. Percy uses a hose that was on top of the roof to extinguish them before they could impact the house. The dodgeballs later blow up the house and the Laistrygonians pursue the heroes hurling more dodgeballs at them.