To determine which statement is incorrect, let's analyze each option based on chemical reactions and principles:
In the borax bead test, Cu^{2+} ions typically produce a green bead in oxidizing flame and a reddish one if conditions favor reduction. Therefore, this statement can be considered correct under specific conditions. However, for standard tests, it's not the usual representation.
In acidic conditions with HCl, H_2S does not precipitate these ions. Cu^{2+} and Ni^{2+} require alkaline conditions to form their respective sulfides. Therefore, this statement is incorrect.
Ferric ions react with potassium thiocyanate to form a complex that gives a characteristic blood-red color. This statement is correct.
When Cu^{2+} ions react with potassium ferrocyanide, a chocolate brown precipitate of copper(II) ferrocyanide is formed. This statement is correct.
After reviewing the options, the incorrect statement is that Cu^{2+} and Ni^{2+} ions give black precipitate with H_2S in presence of HCl solution, because these ions need an alkaline environment to form sulfides.