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Since this is an igniter, the flow rates of GOX and CH4 are very small, which presented some issues with sizing the annulus. To avoid tolerancing issues here, I opted to decouple flow rate from the ASI injector by having upstream orifice fittings with an area less than the annulus and GOX needle. McMaster orifices have flow data for water, which you can use to back out a discharge coefficient (Cd). Then, you can plug this Cd into the equation for choked flow through an orifice to obtain the mdot that this orifice sets. Pointer: the Cd for a straight-edged orifice is usually around 0.7.
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