I have a palm tree in my apt and each time i water small flying bugs scatter around. What is this? How do I get rid of them?

Sounds like fungus gnats if they are dark colored and look somewhat like fruit flies. Let the soil dry out as much as possible between waterings without causing damage to your plant. Gnats like to hang out and eat the decaying material in the moist soil and also breed.
You can also use those sticky yellow traps for plants placed nearest the soil line to trap them.
You can also always change the soil in the spring, hopefully, the new soil does not harbor any of these pest.