D

Step 1: Understand the definition of electric flux ($\Phi$). Electric flux through a surface is given by the formula:
$\Phi = \int \vec{E} \cdot d\vec{A}$, where $\vec{E}$ is the electric field and $d\vec{A}$ is the area vector.

Step 2: For a closed surface like a cylinder, if the electric field ($\vec{E}$) is parallel to the axis of the cylinder, the area vector of the curved surface of the cylinder will be perpendicular to the electric field.

Step 3: In this case, since the electric field is parallel to the axis, the angle ($\theta$) between the electric field and the area vector of the curved surface of the cylinder is 90 degrees.

Step 4: Therefore, the dot product $\vec{E} \cdot d\vec{A}$ becomes zero since $\cos(90^\circ) = 0$. Hence:
$\Phi = \int \vec{E} \cdot d\vec{A} = 0$ for the curved surface area.

Step 5: For the flat ends of the cylinder, the electric field does not pass through them because the electric field lines are parallel to the axis of the cylinder.

Conclusion: The total electric flux through the cylinder is zero because the electric field lines contribute no flux through the surface area of the cylinder.
Therefore, the correct answer is D.