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No, boron is a nonmetal and its simplest oxide, B2O3, is exclusively an acidic oxide.

The supposed reaction between B2O3 and HCl as shown by you takes place spontaneously only in the reverse direction as given below.

BCl3 + 3H2O = H3BO3 + 6HCl

BCl3 is readily and completely hydrolysed by water to boric acid and HCl, and there is no possibility of any reaction between B2O3 and HCl in normal circumstances.

While moving down the group, acidic strength decreases and basic strength increases.

The acidic character of oxides of group 13 decreases down the group, because non-metallic character of elements decreases down the group and metallic character increases.

And we know that oxides of metals are basic in nature and oxides of non-metals are acidic in nature. So acidic character of oxides of group 13 decreases down the group.

For example boron (1st element of group 13) is non-metal, so its oxide is acidic.

Aluminum (2nd element of group 13) shows characteristics of both metal and non-metal, so its oxide shows amphoteric nature.

As we go down the group, indium and thalium (4th and 5th element of group 13) show metallic properties, so their oxides of boron are basic.

Resource from:https://www.quora.com/Is-B2O3-Amphoteric

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