For your training sessions, you will only need a pull buoy.
Flippers and hand paddles are optional.
Flippers can be useful to learn or practice the swim drills and for some kicking sets in the Level 0.
For most of the Pull / Paddles sets, you have the choice to use a pull buoy only or just hand paddles or both together.
Be careful with paddles as they can sometimes put too much stress on your shoulders. Even if you train with paddles at the end of your training, stay focused on maintaining the best technique possible.
If you are not used to swimming equipment, I would recommend starting by using a pull buoy only and then in the longer term, using hand paddles only. Eventually, using both pull buoy and paddles together will give you a stronger workout. Varying equipment reduces the likelihood of repetitive strain injuries and adds interest.
If you are unable to use swimming equipment, feel free to change the pull set to a swim set or add more lengths in your main set instead.