Coulomb's Law is $$F=k\frac{q_1 q_2}{r^2}$$
where $F$ is the force, $k$ is the Coulomb's universal constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the two charges.
Electrons and Charge – Would Coulomb’s Law Change if Protons Were Negative?
chargecharge-conjugationconventionscoulombs-lawelectrons
Best Answer
If protons were negatively charged, and electrons were positively charged, this would be equivalent to flipping the signs of all charges$^*$. Given that, it is quite simple to check that Coulomb's Law obeys charge symmetry, by applying the substitutions $q_1\to-q_1$ and $q_2\to-q_2$. $$F = \frac{kq_1q_2}{r^2} \to \frac{k(-q_1)(-q_2)}{r^2} = (-1)^2\frac{kq_1q_2}{r^2} = F$$ Therefore, there would be no difference if we switched the sign convention of the charges.
$^*$I should note that, technically, switching the charges of protons and electrons would not be entirely equivalent to flipping the signs of all charges, since one could imagine doing this without changing the signs of the charges of other particles, like muons and pions. However, doing this would mean that, for instance, the process $\mu^-\to e^-\nu_\mu\bar\nu_e$ would become $\mu^-\to e^+\nu_\mu\bar\nu_e$, which clearly violates charge conservation.