Even though acrylic and oil paints are non-flammable, it's best to pack them into your check-in luggage rather than carry it in your hand luggage, and risk having an overzealous security personnel confiscate them. If you carry loose tubes, it's advisable to place them in a ziploc bag to prevent accidental leakages. If your paints come in a wooden set, even better! These are great for the travelling artist as the hardness of the box protects your paints and brushes from being squashed and damaged if the contents of your luggage get flung around by rough baggage handlers! The box also doubles up as a table during your plein air sessions.
Your brushes and palette knives should also go in your checked baggage as they could be considered potential weapons.Mediums, turpentine, and mineral spirits are generally considered as hazardous and not be taken on a plane. Buy them at your destination. If in any doubt, try to get hold of a product information sheet and check with the airline preflight.