De Morgan's Theorem applied on the SR Flip Flop characteristic equation
First, let's state De Morgan's theorem as it applies here:
$$A + B = \overline{\overline{A} \cdot \overline{B}}$$

Now let's look at your equation:
$$Q_{n+1} = S + \overline{R}Q_n$$

Taking \$A = S\$ and \$B = \overline{R}Q_n\$ in the above formula gives

$$Q_{n+1} = \overline{\overline{S} \cdot \overline{\overline{R}Q_n}}$$

Which was what we wanted.

As for using only NAND gates, \$\overline{\overline{R}Q_n}\$ is just \$\overline{R}\$ NAND \$Q_n\$, and then your overall equation is just \$\overline{S}\$ NAND \$\overline{\overline{R}Q_n}\$. You can of course define \$\overline{S}\$ as \$S\$ NAND \$S\$, and similarly for \$\overline{R}\$.