AAS will only work on species that can be present in a flame as isolated (unbonded) atoms or ions - hence the name of Atomic Absorption Spectroscopy. This restricts it practically to most metal cations, as there aren't many other species that survive the conditions.
For example, if you want to measure Ca<sup>2+</sup>, then you can't get a decent reading in the presence of phosphate, colloidal aggregates form that don't readily come apart to release the metal cation, even in a flame. You can reduce this problem by forming a complex - the EDTA<sup>4-</sup> complex with calcium is good, [CaEDTA]<sup>2-</sup>, as the ligand combusts in the flame, releasing the calcium cations.
Remember that we are talking about a high temperature flame, so we are talking about an environment with a lot of unusual, and highly reactive species. For example, the C<sub>2</sub> radical is common in a flame, but you won't encounter it in many other places.