Lets start by making this a fission based dragon vs a fusion based dragon so the dragon will have a use for eating all that radioactive material.
Since the dragon will not be able to use uranium ore directly there will need to be a few steps in its digestion process. The first step will be to grind up the ore by chewing and dissolve the uranium ore "yellowcake" in nitric acid in the dragon's stomach to form uranyl nitrate. Then the uranyl nitrate will be passed to the dragon's second stomach where it will be combined with ammonia to create ammonium diuranate. The dragons third stomach will reduce the ammonium diuranate with hydrogen to get uranium dioxide while its 4th stomach will convert that with hydrofluoric acid to uranium tetrafluoride before its 5th stomach oxidizes the results to get uranium hexafluoride "hex".
Once the food is digested it will have to be enriched and molded into a useable form. The hex will be passed via a special organ in the dragon's body consisting of a huge chain of diffusion chambers used to separate the uranium-238 from the uranium-235. The Uranium hexafluoride gas will be cascaded through the diffusion chambers before being passed to the dragon's 6th stomach that chemically removes the fluoride from the hex and transforms it into Uranium dioxide. 435
The Uranium dioxide is then melted and compressed into pellets that are stored in the dragon's reaction chamber.
The dragon's reaction chamber holds the enriched Uranium dioxide pellets close enough to achieve criticality when moderated by the high-pressure water running through it. The high-pressure water is used as both a moderator to keep the reaction critical and as the coolant used to move the energy in the form of heat throughout the dragon's body to its cooling organ, its skin.
Each scale on the dragon has a copper inner side and a steel outer side. The temperature differential between the outside atmosphere and the high temperature, high-pressure coolant water works as a thermocouple to simultaneously cool down the dragon and generate electricity. This electricity is what is used to power the exotic dragon musculature that allows these majestic creatures to hold their immense two-kilometer bodies aloft without being crushed under their own weight.
The dragons breath weapon is powered by pellets generated in its reaction chamber and moved up the dragons esophagus to its breath chamber. When it wants to rain down death on its foes the dragon moves the pellets in its breath chamber together at the same time it opens its mouth and feeds chunks of waste u-238 into its breath chamber. The extreme heat from the breath chamber reaction turns the uranium into a stream of high velocity extremely radioactive uranium plasma. 671