Flute performance requires mastery of complex fingering combinations and register-dependent embouchure control, particularly jet offset adjustment for low-register production. Existing haptic and semi-automated systems do not address both aspects simultaneously through mechanical actuation. To our knowledge, no prior system fully automates fingering while mechanically assisting low-register tone production without requiring embouchure control. We developed a semi-automatic flute robot with an automatic fingering mechanism: fourteen servo motors actuate all keys via wire-based and rack-and-pinion drives in response to MIDI input, enabling performers to produce complete musical pieces through airflow alone. A jet offset assist mechanism rotates the head joint by a calibrated $22^\circ$ during low-register passages, shifting the jet offset toward a low-register configuration without modifying the instrument or embouchure. Fundamental frequency estimation confirmed correct pitch production across the chromatic range (C4--C7) and during musical performance. All key and lever movements were completed within 77.50~ms, corresponding to tempo capacity exceeding standard requirements. Harmonic analysis ($Δ\mathrm{SPL} = \mathrm{SPL}_2 - \mathrm{SPL}_3$) showed a consistent increase in $Δ$SPL for all low-register notes when activated, consistent with the intended jet offset shift. Head joint rotation completed within 40.00~ms. These results demonstrate mechanical feasibility of integrating automated fingering and register-dependent jet offset assistance under controlled conditions.