Multi-mode micropropulsion is a technology that can enable rapidly composable small satellites with unprecedented mission flexibility. To maximize mission flexibility a multi-mode micropropulsion monopropellant must be shared between the chemical and electric propulsion modes. Previous research has identified a promising monopropellant that is both readily catalytically exothermically decomposed (chemical mode) and electrosprayable (electric mode). In this work the linear burn rate of this monopropellant is determined and used to aid the design of a microtube catalytic chemical thruster. Experiments with a pressurized fixed volume reactor are used to determine the linear burn rate. Benchmark experiments use a 13-molar mixture of hydroxylammonium nitrate and water and show agreement to within 5% of literature data. The multi-mode monopropellant is a double-salt ionic liquid consisting of 41% 1-ethyl-3-methylimidazolium ethyl sulfate and 59% hydroxylammonium nitrate by mass. At the design pressure of 1.5 MPa the linear burn rate of this propellant is 26.4 ± 2.5 mm/s. Based on this result, the minimum flow rate required for a microtube with a 0.1 mm inner diameter within the pressure range tested is between 0.12 and 0.35 mg/s.