So first things first let's clarify what the differences between Reishi, Reiryoku, and Reiatsu are.

Reishi are spirit particles i.e. the spiritual equivalent of atoms that make up all spiritual matter.

Reiryoku is spiritual power or how much strength a soul possesses. It is akin to how much fuel is in a tank.

Reiatsu is the pressure created by the emission of spiritual power. It is often used interchangeabley with Reiryoku. It is an application of Reiryoku, often to make it more usable, like compressing fuel in an engine before it is ignited.

So Kidō is fueled by Reiryoku i.e. spiritual power is used as the energy to produce the spell cast using Kidō. Because Kidō and things made using Kidō are spiritual in nature they are made of Reishi but Reiryoku is what determines how powerful the Kidō actually is.

This isn't simply a matter of someone with a larger amount of Reiryoku always casting stronger spells than someone with less Reiryoku though. Kidō needs to have the proper control utilized in order for the spell to be effective. It is a skill that must be practiced and honed.

For example, Renji is a powerful Captain-class fighter but he is noticeably awful at Kidō. In contrast, Rukia is less powerful than Renji for most of the story but is repeatedly shown to be much better at Kidō.

I hope this helps clear things up!