Peel and halve the bananas. Place a wooden stick into each half. Arrange in a shallow pan and cover halfway with rum. Let stand 10 minutes, flipping halfway through. Place on a baking sheet and place in the freezer. Freeze until frozen through and firm, at least 1 hour.
Once the bananas are frozen, leave them in the freezer while preparing the chocolate and coconut. Toast the coconut in the microwave in 30 second increments, stirring occasionally, until evenly golden, about 2 minutes 30 seconds. Toss the flaky salt with the coconut.
Combine chocolate and coconut oil and microwave until melted, about 1 minute. Lightly whisk until the chocolate and oil are combined.
Line a baking sheet with parchment paper. Remove the bananas from the freezer and pat dry if wet. Working quickly, dip each banana in the chocolate, then sprinkle with the coconut and salt, and let dry for a couple of minutes. Serve immediately.