I want to make mono bromination of chloroacetic acid or ethyl chloroacetate ester
To make bromoacetic acid, acetic acid + pyridine + ac2o will yield you it in high yields, then its a simple esterification with EtOH to get ethyl bromoacetate ester
the bromo and the chloro-coumpound should behave in chemical reactions similair, perhaps try 1st the reaction you plan with chloroactetic acid.
A reactions route could be if your really need the bromo compound, NaOH, so you obtain the alcohol, and then you add HBr for the next substitution reaction.
Sounds like you actually want substitution of chlorine for bromine. The classic way to do it is to mix with HBr in presence of iron dust (fresh FeBr3 is usually added like that - it's more efficient if formed in situ). For reference, search "K. B. Yoon and J. K. Kochi, Efficient Conversion of Alkyl Chlorides into Bromides"
Another approach is valid if you want to use said bromide in a substitution reaction: you can just add potassium, sodium or lithium bromide to the reaction mixture as a catalyst, said bromide would react faster than chloride and regenerate itself.
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