 Solution

The aniline nitrogen attacks the ipso carbon bearing fluorine. The aromatic $\pi$ electrons shift to give a Meisenheimer complex, with negative charge delocalized to the positions ortho and para to the attacked carbon. At either nitro substituent, that charge can be delocalized further onto nitro oxygen. Subsequent proton transfer and fluoride elimination restore aromaticity and give the diarylamine.

Both the ortho and para nitro groups stabilize the addition intermediate in 1-fluoro-2,4-dinitrobenzene. The para-mononitro compound lacks the additional ortho stabilization, so addition is less favourable and generally slower under the stated conditions. This comparison concerns stabilization of the addition pathway; the presence of fluorine does not make the reaction an ordinary aliphatic SN2 reaction.