The stable and flexible micromixer (MM) gas-turbine technology is coupled with hydrogen (H2) enrichment to present an oxy-methane combustor that can sustain highly diluted flames for application in the Allam cycle for zero-emission power production. MMs have never been tested under oxy-fuel conditions, which highlights the novelty of the present study. The operability window was quantified over ranges of fuel hydrogen fraction (HF) and oxidizer oxygen fraction OF. The MM showed superior stability, allowing for reducing OF down to 21% (by vol.) without H2 enrichment, which satisfies the dilution requirements (23%) of the primary reaction zone within the Allam-cycle combustor. By comparison, swirl-based burners from past studies exhibited a ∼30% minimum threshold. Enriching the fuel with H2 boosted flame stability and allowed for reducing OF further down to a record-low value of 13% at HF = 65% (by vol.) in fuel mixture. Under these highly diluted conditions, the adiabatic flame temperature is 990°C (1800°F), which is substantially lower than the lean blowout limit of most known technologies of lean premixed air-fuel combustion in gas-turbine applications. The results also showed that H2 enrichment has minimal effect on the adiabatic flame temperature and combustor power density (MW/m3/atm), which facilitates great operational flexibility in adjusting HF to sustain flame stability without influencing the Allam cycle peak temperature or affecting the turbine health. MM combustion with H2 enrichment is thus a recommended technology for controlled-emission, fuel/oxidizer-flexible combustion in gas turbines.