Are the Chakras present in the original Buddha's teachings? I know it is very common these days to associate Chakras with Buddhist meditation, but I couldn't find anything that supports that in the suttas. (I haven't read all suttas)

Did the Buddha himself taught about Chakras or has it been incorporated later in some parts of the world?
There is nothing supernatural about chakras. They are psychosomatic phenomena; they exist only in the subjective world of a person. That's why you can't photograph a chakra, or measure its "field intensity" with some kind of device.

If you inspect your subtle tactile perceptions, you will surely notice feelings in and around your chest, stomach, forehead, eyes, hands, wrists, feet etc. Subjectively, these feelings are not located on the surface of, or inside the body, but rather "in the air" around it.  They are not produced by a contact with an external object, and they are not as sharp as itching or pain. What are they then?

Chakras are somatic projections of our emotional state onto the internal map of the body. They are indicators of what goes on inside our brains, below the threshold of awareness. Some of the emotions most often accompanied by chakra sensations are worry, urge, longing, resentment, irritation but also the positive ones e.g. love, fondness.

In Chinese Mahayana, Buddhism is often taught in combination with Tai-Chi, Qi-Gong, and other forms of "energy management" exercises focused on developing one's psychosomatic skills. The Chinese (also Korean, Vietnamese, etc.) recognize three main chakras: lower dantian (lower abdomen), middle dantian (chest) and upper dantian (head). The Indians  recognize more chakras, but if you think about it, these are just alternative ways to emphasize some of the most important locations in person's subjective space.

Even though Buddha did not mention chakras directly, his various mindfulness practices are essentially chakra exercises. Specifically, kayagata-sati (mindfulness rooted in the body) involves paying constant attention to feelings around throat, chest, solar plexus, lower abdomen, and feet. Similarly, anapana-sati (mindfulness of breathing) involves paying attention to the diaphragm, esp. the sensations experienced around the moment when the breath reverses its direction.

But to answer your question directly, no, Buddha of Pali Canon did not speak about chakras, these and other practices (yoga, tantra) were incorporated later, as people realized their affinity with Buddhism's goal and methods.