Look at the literature for the Cretaceous Austin Chalk. It has varied lithologies that include chalk and other types of limestone. It is a true chalky limestone. Many rocks called chalky limestones in outcrop because of how they weathered so they are not true chalks.
Peter Scholle (in 1970s) was pioneer in describing Chalks as hydrocarbon-reservoirs. During 1970s, a number of volumes of Deep Sea Drilling Project (DSDP) described 'nannofossil chalks' from deep-sea basins all over the world. Incidentally, Chalks from four DSDP Sites were my Ph.D. study material. The discovery and development of Chalk reservoirs from North Sea in 1980s shed more light on them.
Fundamentally, two principal aspects determine chalk formation - 1) Deposition and 2) Preservation. Deep Sea surfaces are infested by plumes of calcareous nannoplankton -Coccoliths - mobile unicellular algae, whose exoskeleton (around a single cell!) called coccosphere formed by intricate spherical arrangement of disc-like structural elements made of ultramicroscopic (sub-micron sized) calcite crystals. These coccospheres upon death and decay of the living cell disintegrate into individual coccoliths and reach sea bottom forming coccolith (primarily) oozes covering 1000s of meters areally and vertically. Enigmatically, these carbonates are DEPOSITED and PRESERVED far below CCD (Calcite compensation depth) presumed to be due to an organic protective cellular sheath around them while deposition and an 'organic' layer separating them from from overlying sea-water. Gradual compaction and (carbonae-) diagenesis of these oozes, which have a micro-porosity of ~40% result in various stages of 'chalk- formation'. Early generation and migration of hydrocarbons into the (ultra-) microscopic pores of these chalks make them excellent petroleum reservoirs.
Since these chalks are very easily vulnerable to physical disintegration (a single monsoon can wash away 100s of meters of sediment) and (chemical) dissolution, their preservation depends upon the overlying sediment cover to protect them.