The cure kinetics analysis of thermoset polymer composites gives useful information about their properties. In this work, two types of layered double hydroxide (LDH) consisting of Mg2+ and Zn2+ as divalent metal ions and CO32− as an anion intercalating agent were synthesized and functionalized with hydroxyapatite (HA) to make a potential thermal resistant nanocomposite. The curing potential of the synthesized nanoplatelets in the epoxy resin was then studied, both qualitatively and quantitatively, in terms of the Cure Index as well as using isoconversional methods, working on the basis of nonisothermal differential scanning calorimetry (DSC) data. Fourier transform infrared spectroscopy (FTIR) was used along with X-ray diffraction (XRD) and thermogravimetric analysis (TGA) to characterize the obtained LDH structures. The FTIR band at 3542 cm−1 corresponded to the O–H stretching vibration of the interlayer water molecules, while the weak band observed at 1640 cm−1 was attributed to the bending vibration of the H–O of the interlayer water. The characteristic band of carbonated hydroxyapatite was observed at 1456 cm−1. In the XRD patterns, the well-defined (00l) reflections, i.e., (003), (006), and (110), supported LDH basal reflections. Nanocomposites prepared at 0.1 wt % were examined for curing potential by the Cure Index as a qualitative criterion that elucidated a Poor cure state for epoxy/LDH nanocomposites. Moreover, the curing kinetics parameters including the activation energy (Eα), reaction order, and the frequency factor were computed using the Friedman and Kissinger–Akahira–Sunose (KAS) isoconversional methods. The evolution of Eα confirmed the inhibitory role of the LDH in the crosslinking reactions. The average value of Eα for the neat epoxy was 54.37 kJ/mol based on the KAS method, whereas the average values were 59.94 and 59.05 kJ/mol for the epoxy containing Zn-Al-CO3-HA and Mg Zn-Al-CO3-HA, respectively. Overall, it was concluded that the developed LDH structures hindered the epoxy curing reactions.