肛 is a bound form, it doesn't stand alone in speech. It appears in compounds like 肛门 (anus), 肛肠 (anorectal), and 肛裂 (anal fissure). Medical/formal register.
⺼ is the flesh-meat radical (left-side form of 肉). 肛 names the anus, a body opening, so the body-part radical is the natural anchor. Compare 肠 (intestine), 胃 (stomach), 腹 (belly), all digestive anatomy under ⺼.
工 (gōng) supplies the sound, tone-shifted to gāng. A pure phonetic loan with no semantic role. Same three-stroke phonetic powers a huge family: 红 (red), 江 (river), 功 (merit), 攻 (attack), 缸 (jar), 杠 (bar).
