Place egg yolks in a separate bowl and set side.
In a medium saucepan, add the flour, sugar, and salt and whisk to combine.
Add the milk, Kailua, and vanilla extract.
Heat the mixture over medium-low heat, whisking constantly.
Once the mixture is warm (but not boiling) pour about 1/4 c. of it into the bowl with the egg yolks and whisk vigorously to temper the yolks.
Immediately pour the egg yolk mixture back into the saucepan and continue whisking over medium-low heat to prevent the eggs from cooking.
Whisk until the pudding starts to thicken, then add chocolate chips and continue whisking until the pudding starts to thicken.
Pour the pudding into a medium bowl and cover with clear plastic wrap (directly on the pudding surface), then poke a few holes in the plastic wrap with a toothpick.
Allow the pudding to cool on the counter for at least 1 hour before refrigerating.
Refrigerate 2-3 hours until the pudding has cooled and is firm.