In the bowl of a stand mixer (or use a hand mixer) with a paddle attachment, cream the cream cheese for 5-6 minutes or until completely smooth and there are no lumps.
Slowly pour in the sugar and flour and mix until just combined.
Add Kahlua, heavy cream, and vanilla and mix on low speed until combined. Slowly increase the speed to high for about 1 minute. Add in the instant espresso powder and mix until the powder has completely dissolved. Scrape the sides and bottom of the bowl and make sure there are no lumps. Give one final mix before adding the eggs.
Add the eggs one at a time and mix just until the yolk disappears into the batter.
Pour the batter into the prepared crust and gently tap the bottom of the pan on the counter to release any air bubbles.
Cover the pan completely with aluminum foil. Add one cup of water into the inner pot of your Instant Pot and add in the trivet,
Place the cheesecake on top of the trivet and set your pot to high pressure for 40 minutes and allow to naturally release for 10 minutes.
Once you can open the pot, remove the cheesecake and allow to cool to room temperature on a wire rack.
Place the cheesecake in the refrigerator to set for at least 6 hours but overnight is recommended.