3 Firm Stackelberg's Oligopoly Game
I assume that you found Firm 3's best response to be 
\begin{equation}
q_3^*(q_1,q_2)=\frac12(16-q_1-q_2).
\end{equation}

The next step would be to solve for Firm 2's best response. Since Firm 2 observes Firm 1's output and correctly anticipates Firm 3's best response, its profit maximization problem is 
\begin{equation}
\max_{q_2}\;(16-q_1-q_2-q_3^*(q_1,q_2))q_2=
\max_{q_2}\;\left(16-q_1-q_2-\frac12(16-q_1-q_2)\right)q_2.
\end{equation}
Solve this problem, you should get Firm 2's best response as a function of $q_1$ only. Denote this best response $q_2^*(q_1)$.

Then, you solve Firm 1's profit maximization, with Firm 1 correctly anticipating the responses of the subsequent two firms: 
\begin{equation}
\max_{q_1}\; \bigl(16-q_1-q_2^*(q_1)-q_3^*(q_1,q_2)\bigr)q_1.
\end{equation}