Is the kinetic energy change of a system (q) equal to the enthalpy change of a system (∆H)?
Under the restrictions of constant $p$, and no non-$pV$ work, we have: 

$$q_p=\Delta H$$

q is the heat flow into the system (postive for flow in, negative for flow out).  However, q is not necessarily the change in the system's kinetic energy.  For instance, suppose you have an endothermic chemical reaction at constant temperature.  Heat will flow into the system.  However, some or all of that heat flow could go into increasing the potential energy of the chemical bonds.  And if the endothermic chemical reaction is accompanied by an increase in volume, some of that heat flow will go into the work needed to expand the system against the external pressure. 

Indeed, if the temperature is constant, and the heat capacity of the reactants and products are the same, then there will be no change in the kinetic energy of the system.  I.e., in that case, none of the heat flow will go into changing the kinetic energy of the system.