Do salt or vinegar in the boiling water help peeling eggs?
A chemist here.

I do add baking soda (Sodium bicarbonate). I am satisfied with it as I never got the white stuck to the shell since I do this. However I can't say that the same eggs would have done otherwise without baking soda.

A possibile reason is that the adhesion of the inner coagulated white to the calcium carbonate shell is modulated by pH. In other words rising the pH of the cooking water by a salt with alkaline hydrolysis - such as baking soda - mimicks the conditions of not extra fresh eggs.*

Note that adding table salt (Sodium chloride) cannot work this way as for the pH is let unchanged. I never tried as for I cannot think of an obvious mechansm for why It should work.**

Concerning adding vinegar (a solution of acetic acid in water): the common explaination is that the shell is softened by dissolution. This would also prevent the inner to shell adhesion as well make the shell itself prone to peel off.

I haven't tried this, neither.

*Eggs which are not very fresh undergo changes resulting in a higher pH and are easy to peel.

**The behaviour of proteins is affected by several parameters such as pH, temperature, ionic content. I cannot exclude that adding table salt is indeed effective.

Starting the cooking in already warm tough not necessarily boiling watet is reported effective too. Rationale is that a fast albume coagulation results in the white to inner shrink without setting on the the film near the shell. Worth a try...