Short answer: Dual-process, mindfulness and flow theory are related by way of attention theory. Two previous posts that may be of interest are "What is the relation between concepts, constructs and measures?" and "How can we realize when a sociological question is impossible to answer?".
This is an apt example of what Thomas Kuhn would have called a question of commensurability. In normal terms, commensurability means the extent to which we can or cannot talk about two or more theories within a common framework, while incommensurability is a fancy way of saying we're comparing apples to farming equipment or dress shirts. In order for two theories in the cognitive sciences to be commensurable, they generally need to satisfy two criteria:
- A common conceptual denominator.
- At least one common construct.
If they satisfy these, then can look for comparable ways of operationalizing and measuring these comparable constructs that can be related to the common concept. In other words, two theories are comparable if they are conceptually related AND conceive of this concept in some at least partially related way.
Dual-process, mindfulness and flow theory: commensurable?
In this case, there is a clear common conceptual denominator, and that is attention, although they differ in how they express that denominator. For Kahneman and Tversky, there is a generalized resource allocation mechanism which produces qualitatively different modes of thinking; for mindfulness, there exists a discrete mental state partly characterized by a particular attentional pattern; for flow theory, there exists another discrete mental state partly characterized by another attentional pattern.
We can therefore talk about these theories in principle, although how effective our ability to do so turns out to be will depend on the merits of the underlying theory of attention. For example, it is meaningful to ask whether meditational practice involves fast or slow thinking, or whether flow states may be considered a form of meditation, and so forth, but only insofar as we can state those questions in terms of a third (attentional) theory. If one of the theories had assumed that attention was infinite, for example, it would be incommensurable with the other two.
A direct three-way comparison of these theories does not exist in the literature. It is possible that someone has directly related one theory to the other for each combination of theories, but it would take three fairly extensive literature searches (dual-process/mindfulness, dual-process/flow, mindfulness/flow). Even if these comparisons actually exist, summarizing them all would almost certainly be beyond the scope of a single SE answer, so I will leave it at this generalized answer.
I think your question about whether these theories are related by neuroimaging evidence is a good intuition, but establishing that similar brain areas are involved in the same behavior does not provide evidence that these are the same, because brain function is dynamic and areas therefore 'have' many functions. It's not just about what areas are active, but also when they are active, in what order they are active, the exact quality of the activity and where the areas are getting input from and sending output to.