We investigated the electrical property of reflective non-alloyed Rh contacts to p-Al0.45Ga0.55N contact layers and the performance of 278 nm flip-chip (FC) LEDs with the Rh and Ni/Au contacts as a function of Mg concentration. The three contact layers contained Mg concentration of 5.7 × 1019 cm−3 (sample A), 1.0 × 1020 cm−3 (sample B), and 1.4 × 1020 cm−3 (sample C). The Rh contacts to the sample A showed non-ohmic behaviour, while the samples B and C were ohmic with contact resistivity of 3.2 × 10−1 and 3.4 × 10−2 Ωcm2, respectively. The FC-LEDs with the sample A, B, and C with the Rh contacts yielded forward voltages of 7.26, 6.24, and 6.30 V, and output power of 10.46, 10.85, and 10.44 mW at 50 A cm−2, respectively, whereas that with the sample C (Ni/Au contact) gave 6.51 V and 6.26 mW. The FC-LEDs with p-Al0.55Ga0.45N (sample D) and p-Al0.61Ga0.39N (sample E) contact layers (with Mg dopant of 8.0 × 1019 cm−3) displayed forward voltage of 7.41 and 8.72 V at 50 A cm−2 and output power of 11.88 and 15.25 mW, respectively. The Wall-plug efficiency of the sample C, D, and E was estimated to be 3.31, 3.21, and 3.50%, respectively. These results show FC-LEDs fabricated with highly Mg-doped p-AlGaN and Rh contact demonstrate reliable performance upon operating at 100 A cm−2.