Given that both of these people are the pinnacle of fate in their realities, we can say that any sign of them being able to even FIGHT each other is a sign of the end times and reality will end the nano-second before they can physically contact each other.
however, if they WERE to meet in some bizarre alternate universe specifically designed to contain them both, the result would like be as follows:
They would meet in a sun-baked western-style bar (where else would both of these individuals meet?)
and, upon seeing each other, and feeling the urge to cmopare penis sizes, the following events occur in short order
Duke Nukem, seeing a threat to his babe collection, begins unloading every round of every gun he has, in one singular moment, along with a hefty Duke-Boot aimed at Mr. Norris.
Chuck Norris, seeing a threat to his ability to pull his old flame / busty bar wench / delete as appropriate, simultaniously throws glasses, beer bottles, tables, chairs and pool cues (may not in fact be limited to those exact things, I suspect a projectile-thrown cow may be involved somewhere) in one singular moment the same moment, in fact, that he begins one of his most deadly roundhouse kicks towards Mr. Nukem.
all these forces meet in one specific point in space and time, where Duke's boot meets Chuck Norris'. and the sum total kinetic impact travels through them like a wave upon a shore unable to harm either of them, but as it reaches their extremities, breaks upon reality like a tidal wave and detonates the surrounding area like a small nuclear explosion, leaving nothing but dust, ashes and the pair looking at each other quite sheepishly before attempting to find another bar.
