Does 2-chloro-1,3-dinitrobenzene show resonance?
2-chloro-1,3-dinitrobenzene is shown below:



I believe your question is referring to the lack of conjugation between the nitro groups and the aromatic ring. this is best shown in an X-ray crystal structure such as this one:



https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=722415

Due to the sterics between the nitro groups and the chloro substituent, the nitro groups cannot adopt a conformation planar with the ring. This prevents the $\pi$ system of the nitro group from achieving substantial overlap with the $\pi$ system of the ring and prevents full conjugation of the electrons. The sterics are better seen in a spacefilling view:



So, it is not the chloro group that is out of the plane, but rather the nitro groups.