Identify the concept

The classical method used to distinguish and separate primary ($1^\circ$), secondary ($2^\circ$), and tertiary ($3^\circ$) amines is the Hinsberg test.

Reagent used in Hinsberg test

The reagent in the Hinsberg test is benzenesulphonyl chloride (often written as benzene sulphonyl chloride), in the presence of alkali.

How separation occurs

• Primary amine reacts with benzenesulphonyl chloride to form a sulphonamide containing an acidic hydrogen. It dissolves in alkali due to salt formation.
• Secondary amine also forms a sulphonamide, but it has no acidic hydrogen, so it is insoluble in alkali.
• Tertiary amine does not react under these conditions and remains insoluble, but it can dissolve in dilute acid as an ammonium salt.

Thus, these amines can be separated using benzene sulphonyl chloride.

Check the options

• A: Chloroform and KOH
  This is used in the carbylamine test for primary amines, not for separating all three. Incorrect.

• B: Acetyl amide
  Not a reagent for separating primary, secondary, and tertiary amines. Incorrect.

• C: Benzene sulphonic acid
  The required reagent is benzene sulphonyl chloride, not the acid. Incorrect.

• D: para-Toluene sulphonyl chloride
  Sulphonyl chlorides such as $p$-toluenesulphonyl chloride can also be used analogously for such differentiation/separation. This is the best correct option among those given.

Final answer

Therefore, the correct option is: $\boxed{D}$