This is an aeolian sandstone, deposited in an arid environment. A modern day equivalent would be the Sahara which is 3000 x 1000 miles in size.
There is no problem for desert sand to come from hundreds or even thousands of kilometers away. Wind does that to the land if there is no vegetation.
The colours you see could be primary but are more likely diagenetic, .i.e. post-depositional leeching effects of weathering and groundwater (yes it does rain sometimes even in the Sahara).
You must be careful with interpreting 3D structures from 2D photos. In aeolian sands there will be a lot of steep cross-bedding that can go in different directions and might look like deformation from some angles. Dunes move, get partially eroded and then covered again with new sand blown from a different direction. Locally there could perhaps be soft sediment deformation especially if there have been occasional episodes of torrential rain or flash floods.
Desert sands can be identified by the nature and sorting of the sand grains, by wind erosion of occasional pebbles, by the already mentioned steep crossbedding (steeper than for sand formed under water). They can be found associated with conglomerates deposited by ephemeral streams, and with silts, clays and evaporites deposited in sabkhas and playa lakes. Sometimes one can find the odd fossil, or tracks made by animals. In the playa lake clays you often see desiccation mud cracks and perhaps some fossil plant roots.
All of this tells you right there and then that, whatever else, these sands were obviously not deposited by a global flood.
To deposit and preserve such thicknesses you are looking at subsiding basins. The Earth crust is not rigid and can flex up and own in repsonse to tectonic forces and bulging in the underlying mantle. This can create space for very thick sediment piles. The weight of these sediments adds to the subsidence (but doesn’t cause it).
After the period of desert sedimentation, if the subsidence is still ongoing and sea levels rise, all of this can eventually be covered in younger, marine strata. That way it gets preserved until at a much later time the region gets uplifted, eroded and it all gets exposed again - for us to study and marvel at.
By the way, such sands can be excellent hydrocarbon reservoirs because of their grain size and good sorting, as well as the absence of clay layers that can cause permeability problems in water-lain sandstones. Very famous are the Permian Rotliegend Sandstones that hold large gas reserves below the North Sea and surrounding land areas. Because of that, such sands have been extensively studied in outcrop, in modern analogs and in boreholes. They are very well understood.
