How do I convert salinity measured in mg/L Cl into parts per thousand as NaCl?
$$\pu{1 mg L-1} = \pu{1 ppm} = \frac{1}{1000}\cdot\pu{ppt}$$

or

$$\pu{1 ppt} = \pu{1000 ppm}$$

For example:

$$\pu{10 ppm} = \frac{10}{1000}~\pu{ppt} = \pu{0.01 ppt}\tag{1}$$
$$\pu{5 ppt} = 5\cdot\pu{1000 ppm} = \pu{5000 ppm}\tag{2}$$