Chemical bonds are on the scale of eV---the cost to liberate an electron from a hydrogen atom is 13.6eV, for example. So the best you can hope for, in a chemical reaction, is a change in mass of the scale of 10s of eV / c^2.
In comparison, a single proton weighs 938 MeV = 9.38e+8 eV. So the fraction of the mass that is converted into energy is on the scale of 1e-7.