Are flagella an STD?

No, flagella is not a sexually transmittable infection. Flagella (singular = flagellum) are tail-like appendages found on the body of some eukaryotic and prokaryotic cells to provide movement in motile cells as well as functioning as a sensory structure detecting chemical and temperature changes.

But, Trichomonas vaginalis is a flagellated protozoan and causes TRICH.