A better alternative to the use of potentially hazardous oxidizers is an NMR tube cleaner (right). It is an apparatus which uses a vacuum to flush solvent and/or a detergent solution through the entire length of the NMR tube.
In this apparatus, the NMR tube 1 (with the cap 3 fixed to the base of the NMR tube), is placed upside down on the apparatus. The NMR tube fits over an inner tube 5 linked to the solvent reservoir 6. The NMR cap rests on the outer tube of the apparatus 4. A vacuum is applied (usually via a water aspirator via the vacuum inlet). The NMR tube cap forms a vacuum seal. Solvent 7 is drawn from the solvent reservoir 6 and is forced to the base of the NMR tube and flushes the NMR tube out 9 with solvent cleaning it. Note to complete the vacuum a flask is attached to the NMR tube cleaning apparatus.
This sort of apparatus is commercially available, though it is costly and easy to destroy by shattering or breaking off the cleaning tube. Equivalent designs may be assembled from ordinary labware as well.