C

The magnetic flux ($\Phi$) is given by the equation:
$$\Phi = B \cdot A$$
where B is the magnetic field (measured in Teslas, T) and A is the area (measured in square meters, m$^2$).
The dimensions of magnetic field B can be expressed as:
$$[B] = [F][q]^{-1}[d]^{-1} = \frac{M L T^{-2}}{A} = M L T^{-2} A^{-1}$$
Therefore, dimensions of magnetic flux are:
$$[\Phi] = [B][A] = (M L T^{-2} A^{-1})(L^2) = M L^2 T^{-2} A^{-1}$$
Hence, the correct dimensional formula for magnetic flux is option C: $ML^{2}T^{-2}A^{-1}$.