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The reionization of the hydrogen in the Universe is thought to have completed by redshift $z\simeq5.5-6$. To probe this era, galaxy observations in the Subaru Deep Field (SDF) have identified more than 100 galaxies at $z\simeq6$, many spectroscopically confirmed through follow-up observations. We model the spectral energy distributions (SEDs) of 13 SDF galaxies with the CIGALE and Dense Basis codes using available optical/IR data. Modeling deep IR photometry has the potential to constrain the galaxy's Lyman continuum (LyC) escape fraction (\fesc). We use the modeled nebular emission lines and find that the implied escape fractions ranges from \textbf{0 to 0.8 with a median of $\sim$0.35 for Dense Basis and $\sim$0.55 for CIGALE.} Significant uncertainties in the data exist, so that fitting results in a large range of \fesc\ for individual objects. The implied median \fesc-values may be high enough for galaxies to finish reionization by $z\sim6$. Furthermore, we find no strong trends between the UV-slope $β$ or \EBminV with model \fesc. If true, the lack of trends suggest that other factors besides nebular emission or dust extinction could have led to LyC escaping, such as the presence of holes in the ISM with sufficiently wide opening angles from outflows of supernovae and/or weak AGN, resulting in a range of implied \fesc-values depending on the viewing angle of each galaxy. The current \textit{HST, Spitzer} and ground-based photometric and model errors for the galaxies remain large, so IR spectroscopic observations with the \textit{James Webb Space Telescope} are needed to constrain this possibility.