Fluorescent proteins are valuable tools as biochemical markers for studying cellular processes. Red fluorescent proteins (RFPs) are highly desirable for in vivo applications because they absorb and emit light in the red region of the spectrum where cellular autofluorescence is low. The naturally occurring fluorescent proteins with emission peaks in this region of the spectrum occur in dimeric or tetrameric forms. The development of mutant monomeric variants of RFPs has resulted in several novel FPs known as mFruits. Though oxygen is required for maturation of the chromophore, it is known that photobleaching of FPs is oxygen sensitive, and oxygen-free conditions result in improved photostabilities. Therefore, understanding oxygen diffusion pathways in FPs is important for both photostabilites and maturation of the chromophores. We used molecular dynamics calculations to investigate the protein barrel fluctuations in mCherry, which is one of the most useful monomeric mFruit variants, and its GFP homolog citrine. We employed implicit ligand sampling and locally enhanced sampling to determine oxygen pathways from the bulk solvent into the mCherry chromophore in the interior of the protein. The pathway contains several oxygen hosting pockets, which were identified by the amino acid residues that form the pocket. We calculated the free-energy of an oxygen molecule at points along the path. We also investigated an RFP variant known to be significantly less photostable than mCherry and find much easier oxygen access in this variant. We showed that oxygen pathways can be blocked or altered, and barrel fluctuations can be reduced by strategic amino acid substitutions. The results provide a better understanding of the mechanism of molecular oxygen access into the fully folded mCherry protein barrel and provide insight into the photobleaching process in these proteins.