Electromagnetic interference (EMI) shielding coating materials with thicknesses in the microscale are required in many sectors, including communications, medical, aerospace and electronics, to isolate the electromagnetic radiation emitted from electronic equipment. We report a spray, layer-by-layer (LbL) coating approach to fabricate micron thick, highly-ordered and electrically-conductive coatings with exceptional EMI shielding effectiveness (EMI SE >4830 dB/mm), through the alternating self-assembly of negatively-charged reduced graphene oxide (RGO) and a positively-charged polyelectrolyte (PEI). The microstructure and resulting electrical properties of the (PEI/RGO)n LbL structures are studied as function of increasing mass of graphene deposited per cycle (keeping the PEI content constant), number of deposited layers (n), flake diameter and type of RGO. A strong effect of the lateral flake dimensions on the electrical properties is observed, which also influences the EMI SE. A maximum EMI SE of 29 dB is obtained for a 6 um thick (PEI/RGO)10 coating with 19 vol.% loading of reduced electrochemically-exfoliated graphene oxide flakes with diameters ~3um. This SE performance exceeds those previously reported for thicker graphene papers and bulk graphene/polymer composite films with higher RGO or graphene nanoplatelets contents, which represents an important step towards the fabrication of thin and light-weight high-performance EMI shielding structures.