To determine the gassiness of the seam, we calculate the gas emission rate per tonne of coal produced.
Given 1000 tonnes of coal produced per day and an inflammable gas emission rate of 14000 m$^3$ per day, the gas emission rate is $\dfrac{14000}{1000} = 14$ m$^3$/tone.
Additionally, the percentage of inflammable gas in the general body of the air is 0.14%, which is relatively low but still significant. In coal mining (e.g., Indian mining regulations), gassiness is classified as: Degree I (<1 m$^3$/tonne), Degree II (1-10 m$^3$/tonne), Degree III (10-25 m$^3$/tonne), and Degree IV (>25 m$^3$/tonne).
Since 14 m$^3$/tonne falls in the range of 10-25 m$^3$/tonne, the seam is classified as Degree III. The percentage of gas in the air supports the need for ventilation but does not change the classification.
Thus, the correct answer is Degree III.