I’m not very knowledgeable about hydrology, but I can think of two ways to get reliable annual flooding and two ways to get a desert for your river to flow through.
The flooding can depend either on snowmelt or on seasonal rains. The desert can be produced either by the
high pressure belt in the horse latitudes or by a rain shadow. Mostly that’s easier with the river running between two latitudinal bands of climate (i.e. north or south), but you might like to look into the way that a seasonal analogue of the katabatic effect results in the Tibetan plateau producing the
monsoons of South Asia.