This is referring to Charles' Law.
'The volume of an amount gas at constant pressure is directly proportional to the temperature'.
In other words, the greater the temperature of a gas, the greater the volume (and vice versa).
Essentially, when the gas is heated, it has more kinetic energy (gas molecules move around more more quickly). In turn, the gas expands and occupies more space (hence the increase in volume).
So the flask heats up due to the exothermic reaction, leading to an increase in volume due to increase in kinetic energy. As per Charles' Law.