Is the activation barrier of a reaction related to the free energy or heat of formation of its reactants?
They are certainly related, but not necessarily the same. If all bond-breaking and forming would be sequential than the activation energy would equal the bond-breaking energy.

However, it is possible in some reaction mechanisms that the forming bonds 'donate' energy to the break-up and therefore the overall activation energy will be lower. An example is the reaction of hydrogeniodide to hydrogen and iodine show in the figure below. Instead of a full dissocation, two molecules of $\ce{HI}$ line up and the breakup occurs simultaneously with the formation of the new bonds thus allowing a lower energy level.



The only thing you can safely say is that the sum of breaking energies is an upper bound for the activation energy, because single atom level is 'as bad as it gets' (excluding nuclear reactions).