NB: There is a related question – What kind of planet could have giant sand worms? – but this one is concerned specifically with the sand. Giant sand worms would be
Assuming a terrestrial planet with a dry atmosphere (the composition is unimportant unless other conditions are dependent), an average surface temperature above freezing, and any other conditions necessary for desertification to progress to the point its status as an arid "desert planet" isn't in question, what conditions are needed to maximize the depth of the sand in the planet-spanning desert?
Here on Earth sand depth has been measured to 43 metres in the Sahara, while dunes in the Namib have been are known to reach as much as 100 metres in height (with a maximum mean depth of 30 metres for surrounding sand). Mesozoic and Paleozoic ergs have reportedly been measured in the hundreds of metres of depth (mean), but it has been suggested these may have been sequences of ergs migrating and stacking over geologic time. (Source: Aeolian Sand and Sand Dunes, pp 155) If hundreds of metres is achievable on a planet with vast liquid oceans and mountains like the Himalayas, would a desert planet be able to boast dune seas tens of kilometres deep?
(There is probably an upper limit to how much sand-on-sand pressure could be endured before the deepest sand begins to undergo lithification or diagenesis and stops being sand, but I have not been able to find what that is.)
Planetary composition, mass, size, surface gravity, stellar parent, age, and so on can be modified as needed within the assumption above. The best answer would be able to specify planetary properties that are likely to produce deserts deeper than other combinations of properties.