New types of magneto-rheological fluids are increasingly being developed lately, but there is a dearth of information on the performance of commonly used rheological models for emerging MRFs such as carbonyl-iron particles (CIP) paraffin-oil-based MRF. This work aims to investigate the performance of some rheological models for application in predicting shear stress and yield strength in an emerging MRF suitable for flow-mode applications. CIP, low viscosity paraffin oil, and lithium grease were used as magnetic particles, carrier fluid, and additives, respectively, to prepare the MRF. Based on different mixing proportions determined with the Taguchi method of experimental design, sixteen samples were prepared following a standard procedure. For each sample, the values of viscosity and shear stress were determined using a viscometer and rheometer, respectively, with an incorporated self-developed magnetic device. By fitting the data and using the multi-objective nonlinear programming solver in Micro-soft Excel to determine optimum parameters for each model, the Bingham Model, Herschel–Buckley Model, Casson Model, Cross models, and Power-law were used to model the experimental data. Predicted shear stress values and yield strength were then analyzed using ANOVA at a 5% confidence level. The relative errors were determined using RMSE, Mean Square Error, and Mean Absolute Error. There was a significant variation in the predicted outcomes of all the models. Overall, all the models gave relatively acceptable results. However, the Herschel-Buckley model gave the best results, while the Casson model gave the worst results, judging by their values of errors. It is shown that the Herschel-Buckley model should be best used for predicting the rheological characteristics of CIP and paraffin oil-based MRF.