In pop, rock and R&B styles of singing the quick passages you are referring to are commonly known as "riffs." Riffing is something that is very popular. In the operatic and other classical vocal genre, riffing is known as Coloratura. Fast singing is something that some singers seem to be able to do quite naturally, but others seem to struggle with. In order to sing coloratura well, the voice must be very flexible, the larynx at a comfortable speech-level (floating, not jammed up or locked down), and there must be a perfect balance of cord connection and air flow.
The quick riffs should sound natural and spontaneous. The only way to develop this sound is to practice the passages at more moderate speeds, note by note, and gradually increase the tempo. The goal is to maintain your speech-level posture, feel no strain or excess breath pressure beneath the cords, and feel as though the passage is connected from bottom to top (rather than flipping into a disconnected, falsetto type of production in the higher ranges).
After your technique has been developed to a certain degree where you are able to sing comfortably at your speech-level, it is advisable that you practice singing quick passages.
This is tough ask at the first glance but I found that once you start getting into the flow it becomes quite easy.