Store it in the fridge when not consuming. If possible, lay it on its side. It will last for a good 2-3 months if stored properly even after you open it.
Give it a really nice shake before serving. Like ... more than you think. Shake it until all the spices have fully blended. If there is a thick clump on the top of the bottle keep shaking it until it completely blends. That clump is simply the coconut cream separating.
It can be served chilled or over ice.
Too thick? Take it out of the fridge for a few minutes and give it another shake.
Wish it had more of a kick? Go ahead and add a little more rum, whiskey, cognac or brandy. Whatever floats your boat. Just remember .... you can always add, but never take away. So, just add a little before adding again to your liking.
Traveling? You can absolutely take these bottles with you on your flight. You must check them in and they must not be opened. So, keep them sealed and I would recommend freezing your bottles before packing them in your luggage. You can purchase cold bubble mailers to store them in so the condensation doesn't wet your other personal items. I would also recommend checking directly with your airline to ensure you can bring your bottle in your checked in luggage.
Looking to store them for a longer time? You can absolutely freeze your bottle until you are ready to consume. This will preserve the freshness of your coquito and it even turns into a yummy ice cream if you freeze it in an appropriate plastic container.