Multi-mode micropropulsion is a potential game-changing technology enabling rapidly composable small satellites with unprecedented mission flexibility. Maximum mission flexibility requires propellant that is shared between the chemical and electric propulsion systems. 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 to aid design of the microtube catalytic chemical thruster. A pressurized fixed volume reactor is 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 used for designing the muli-mode propulsion system is 22.8 mm/s. Based on this result, the minimum flow rate required is 0.25 mg/s for a feed tube with a 0.1 mm inner diameter and 2500 mg/s for a feed tube with a 10 mm inner diameter.