As a first approximation, you can calculate how much air is aspirated at the inlet. For this one needs to know the engine speed and volumetric efficiency at that point. The theoretical volume aspirated is the engine displacement x speed / strokes (2 for 2 stroke and 4 for 4 stroke). This flow is reduced by the volumetric efficiency.
Once you have this one has to compute the exhaust gas composition (H2O, CO2, CO, NOx, N2 and O2) and determine the exhaust gas temperature. From here one can get a good estimate of what the volume flow is (from the gas properties). The flow speed, of course, is the volume flow divided by the cross section.
The mass flow is simple, as the output is equal to the combined inputs (aspirated air + fuel) There is a little mass "lost" due to leaks past valves and cylinder rings., but this can usually be ignored.
Exactly this approach (ma+mf=me) has been implemented in the IMO MARPOL NOx Technical Code 2008. The idea is simple: what enters the engine in unit time-air for combustion and fuel oil (estomated from SFOC). What gets out in unit time-exhaust gases and kinetic energy of rotation; energy has no mass). If ma+mf>me then the engine will gain weight, if ma+mf
You may simulate the engine combustion by using a chemical equilibrium code which will give the mole fractions and also mole numbers of the species i.e exhaust gas composition.
Exhaust flow for a particular condition can be calculated using engine simulation code such as GTPower. John Heywood's "Internal Combustion Engine Fundamentals" shows a relatively simple quasi-steady-state approximation for engine cylinder air flow based on cylinder volume, engine speed, and air density at a constant air temperature.
Experimentally, in addition to the afformentioned experimental measurement of air-flow and fuel-flow, exhaust gas flow can also be calculated by measuring air-flow and measuring exhaust oxygen content with a wide-band zirconia oxygen sensor. An oxygen balance calculation based upon oxygen sensor data can then be used to calculate fuel mass flow fairly precisely from air mass flow even for highly transient engine operation.
Do you know the displacement of the engine? And the RPM it's running on?
If displacement is L cu. meters and rpm is R, you get L * R cu.meter per minute coming out of the engine if it's a 2 stroke, L * R/2 if it's a 4 stroke.
More details: Method Calculation of Exhaust Gas Flow Rate in an Internal Combustion Engine
In order to determine, exhaust gas flow rate in mass or volume, the formula for total mass of exhaust gas is ma (mass of air)+ mf (mass of fuel). mass of air is determined by orifice meter at inlet connected to U- tube manometer. Volume of fuel is determined by connecting a measuring fuel pipe connected to fuel tank before entering to cylinder and later converted to mass. After getting the total mass, this can be converted to volume. Heat lost due to exhaust gas is given by (ma+mf) cpg (Tg1 -Ta) here cpg is specific heat of exhaust gases and Tg1, Ta are temperatures of exhaust gas just measured at outlet of engine and Ta is atmospheric temperature.