Step 1: Apply Hardy-Schulze rule.
According to the Hardy-Schulze rule, the coagulating power of an ion depends on the magnitude of charge carried by the ion having charge opposite to that of the sol.
Here, the sol is positively charged, so negatively charged ions (anions) will cause coagulation.
Greater the negative charge on the ion, greater is its coagulating power.
Step 2: Compare the charges on the ions.
For ion I:
\[
[Fe(CN)_6]^{4-}
\]
Charge magnitude:
\[
4
\]
For ion III:
\[
SO_4^{2-}
\]
Charge magnitude:
\[
2
\]
For ion II:
\[
Cl^{-}
\]
Charge magnitude:
\[
1
\]
Step 3: Arrange according to coagulating power.
Since coagulating power increases with increase in magnitude of charge:
\[
[Fe(CN)_6]^{4-}\gt SO_4^{2-}\gt Cl^{-}
\]
Thus,
\[
I\gt III\gt II
\]
Step 4: Final conclusion.
Hence, the correct order of coagulating power is
\[
\boxed{I\gt III\gt II}
\]