We present the results of very long baseline interferometry (VLBI) observations of gamma-ray bright blazar S5 0716+714 using the Korean VLBI Network (KVN) at the 22, 43, 86, and 129 GHz bands, as part of the Interferometric Monitoring of Gamma-ray Bright AGNs (iMOGABA) KVN key science program. Observations were conducted in 29 sessions from January 16, 2013 to March 1, 2016, with the source being detected and imaged at all available frequencies. In all epochs, the source was compact on the milliarcsecond (mas) scale, yielding a compact VLBI core dominating the synchrotron emission on these scales. Based on the multi-wavelength data between 15 GHz (Owens Valley Radio Observatory) and 230 GHz (Submillimeter Array), we found that the source shows multiple prominent enhancements of the flux density at the centimeter (cm) and millimeter (mm) wavelengths, with mm enhancements leading cm enhancements by -16±8 days. The turnover frequency was found to vary between 21 to 69 GHz during our observations. By assuming a synchrotron self-absorption model for the relativistic jet emission in S5 0716+714, we found the magnetic field strength in the mas emission region to be ≤ 5 mG during the observing period, yielding a weighted mean of 1.0 ± 0.6 mG for higher turnover frequencies (e.g., >45 GHz).