Why does phosphate rock contain uranium?
To understand why sedimentary phosphate rocks (hereafter referred to as phosphorites) have elevated uranium contents we first need to understand what are they made of and why do they form in the first place.

Phosphorites are rocks that are made of apatite, a mineral with the formula $\ce{Ca5(PO4)3(F,Cl,OH)}$. This mineral (especially the OH variant) is one of the main constituents of skeletons of living organisms. The hard mineralised part of your teeth and bones are made of apatite, for instance.

Skeletons of dead marine animals (e.g. fish) are deposited on the ocean floor as apatite. The source of apatite need not be biogenic: it can also be sourced from igneous or hydrothermal activity occurring on the ocean floor, or derived as clastic material from the continents. The end result, is the deposition of apatite as phosphorites.

An important property of apatite is that it can accommodate some uranium. The mechanism is not yet completely understood, but it's most likely the incorporation of $\ce{U^4+}$ in the mineral structure of apatite, replacing calcium. Now here's the interesting part - uranium in sea water is mostly present as $\ce{U^6+}$ (in the form of the uranyl ion). The uranyl ion is more soluble than $\ce{U^4+}$ so it mostly remains in solution in the sea water. But, as we mentioned earlier, apatite deposits form by the decay of dead marine animals. This accumulation of decaying organic material reduces the $\ce{U^6+}$ to $\ce{U^4+}$, facilitating its incorporation into the apatite structure.

That's only one side of the coin. Apparently $\ce{U^6+}$ can also be adsorbed on apatite grains. This is even used in some cases to stop uranium contamination from migrating through soil - by adding apatite to it in order to immobilise it.

Whatever the exact process (or combination of processes) that make uranium such a good friend of apatite, the end result is that apatite (and rocks containing it) is enriched in uranium relative to its environment.