Why doesn't KI(aq) react with HCl(aq)? When concentrated sulfuric acid is added to anhydrous potassium chloride and the fumes produced are bubbled into aqueous potassium iodide solution, the observed solution would be colourless solution.

I think the first reaction is:
$$\ce{2KCl(aq) + H2SO4(aq) -&gt; K2SO4 + 2HCl(g)}$$

I assumed the second reaction would be:
$$\ce{HCl + KI -&gt; KCl + \frac{1}{2}I2 + \frac{1}{2}H2 }$$

However the second reaction is wrong according to the answer book as $\ce{HCl}$ won't react with $\ce{KI}$. From what I know, $\ce{Cl}$ is a stronger oxidising agent than $\ce{I}$, so shouldn't $\ce{I-}$ in $\ce{KI}$ be oxidized to $\ce{I2}$? I am an A-levels student so would appreciate a simpler answer.
In your first reaction, you added concentrated sulfuric acid to anhydrous potassium chloride. In your equation, you wrote $\ce{KCl (aq)}$, which is incorrect. Under dilute conditions, that reaction would not take place because all reagents and products would be in aqueous ionic state, meaning there is no reaction.
In your second reaction, the equation is completely wrong. It is true that elemental $\ce{Cl2}$ a stronger oxidizing agent than elemental $\ce{Br2}$ or elemental $\ce{I2}$. But in current situation is ionic $\ce{Cl-}$ versus ionic $\ce{I-}$ where both are aqueous. If all reagents are in ionic form and expected products are also ionic, there is no reaction. See your reaction below:
$$\ce{H+(aq) + Cl-(aq) +K+(aq) + I-(aq) &lt;=&gt; H+(aq) + I-(aq) +K+(aq) + Cl-(aq)}$$
There is no gas, liquid or solid formed, but all ions. Therefore, there is no reaction.