First, I would like to say that dual model systems are simplistic with the goal being to reduce limitless actuality (plural objects, multiplicity) into a binary frame, which binary frame is the realm of choice-making: this and not that, this and not those.

So in Kahneman, symbolic System 1, sometimes called intuitive and hard to change ("inert"), is binary as it's defined around how action is taken. And symbolic System 2, sometimes deemed studied ("volatile"), also is binary, as it too is concerned with how action is taken.

These are both, in fact, self-protective systems of choices: the difference in choice-making is time, observation, and deliberation of choice-making. Kahneman is pointing out effects of these symbolic systems of fast or slow choice-making. [1]

Mindfulness, if we take a Kabat-Zinn definition, is "moment-to-moment, non-judgmental awareness" (Google, 2007, youtube). Anālayo also writes this about "sati" (which Pāli word is commonly translated as "mindfulness" in English), from Sattipathana, The Direct Path to Realization:

Multiplicity, plural objects, is the terrain of mindfulness.

Though as a rationalized choice for well-being, mindfulness in that moment of deliberate choice, is action of a symbolic System 2. (This concerns not infants, who may meet the definition of mindfulness in a symbolic System 1 sense and during the time immediately following birth and preceding habituation of feeding and care).

To step away from the symbolic systems and consider physiology (unless one considers the body symbolic, too), then mindfulness (developing a mind non-judgementally aware of plural objects (multiplicities of feelings, thoughts, sensations) is also shown to affect parasympathetic "choices" of the body, such as rate of breath and blood pressure (such as the effect of lower blood pressure simply by choosing non-judgemental awareness of objects). Mindfulness is there, too, non-controlling, non-choosing: Sweaty palms? Okay, sweaty palms.

So mindfulness begins as a specific training as a choice in the symbolic System 2 family. In buddhism, notions of release/final release/full awakening/enlightenment-- these notions suggest the mind is without suffering if equanimous, and some buddhist traditions train that this equanimity is inherent. [2]

What do you think?

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[1] To go to page 35 at the beginning of "Thinking, Fast and Slow" (first ed., paperback, FSG), top two paragraphs, the two systems are described in their practical implications: System 2 activity follows directions in response to mental overload, a parallel to the electrical circuitry of a house is made. Whereas System 1 is defined as the terrain of self-protective actions and the example of being in a car accident is given: "You will find you have responded to the threat before you became fully aware of it."

[2] Pali tradition (Malunkyaputta Sutta) "Not impassioned with ideas, knowing an idea with mindfulness firm — dispassioned in mind, one knows and doesn't remain fastened there. While one is knowing an idea — and even experiencing feeling — it falls away and doesn't accumulate. Thus one fares mindfully. Thus not amassing stress, one is said to be in the presence of Unbinding; Zen/Chan tradition: "What difference is there in our Buddha nature?" ~ Hui Neng, and "The so-called "clear mind" refers to the pure mind devoid of passions," Shen-yen on the Platform lesson of Hui Neng]; "And inspire me that with mindfulness and alertness, born from thoughts ultimately pure (...) the ways leading to personal liberation,"~ The man from Onion Valley in the foundation of all good qualities (ca. 1400s).

[edit x1: typos]