In a small bowl, whisk together pineapple juice, 3/4 cup water, the lime juice, salt, and sugar until sugar dissolves. Stir in chile flakes. Pour seasoned juice into a spouted measuring cup, then into 8 (1/4 cup) popsicle molds* to fill each by two-thirds (before each pour, stir liquid to distribute chile flakes). Add enough pineapple to each so liquid rises to the fill line.
Freeze pops until slushy (don't insert sticks yet), about 2 hours. With a chopstick, stir up fruit and chile flakes to distribute evenly. Insert sticks and freeze pops until solid, at least 4 hours more.
To remove popsicles from molds, either let sit at room temperature 5 minutes or run under warm water 10 to 15 seconds.
*We used 1/4-cup cylindrical molds from Aymuna ($99/8 molds; amazon.com).
Make ahead: Up to 2 weeks, frozen.