TLDR; EP and DST share the perspective of their content matter as dynamic, systems-based, and relational.
Part of what I taught in my doctoral course brings up the connection between EP and DST, why do they seem to work well together? Here’s a general and concise answer to this question:
EP connects well with DST in my opinion because EP takes at its ontological core a relational (as including, implicating, both the environment and organism together as a system) and dynamic perspective on the ongoings of the world where organisms are involved. Dynamic Systems Theory also takes its subject matter as dynamic (perhaps obviously) as the analyses that DST contains require dynamic measurements to be carried out. Since I am an Ecological Psychologist, I will tell you that DST works the best with relational phenomena, evidenced by experiments on e.g. movement where we would be less likely to use the literal three-dimensional points of say a hand as the sole basis of an analysis (because it is a component and not a relation) but more likely e.g. an angle between one limb and another (not excluding that three-dimensional positions can be used to calculate a relational measure). However, cognitivists have argued that DST works fine with the former kinds of measurements too where a component is the basis of a measurement, so it may be a preconceived idea kind of thing. Then there is the third part, and that is that EP takes the entire system as the content matter of psychology, which includes the environment. To explain behavior we cannot just talk about the human, or worse, only the inside of a human. We need to understand the entire organism-environment system to understand why a particular behavior arose/emerged. Dynamic Systems Theory (again, perhaps obviously) shares the perspective that a system of many components, due to rules of engagement (relations), can result in the most complex of collective behaviors, given repetitions over time (partly summed up by the term emergence). However, some argue here that the brain has many components and can also be seen as a system, and based on the rules of DST this is allowable. Which is why DST is called a-theoretic, and its collection of methods and analyses really only require a numerical time-series, which is why I can work with some colleagues without a shared ontological/epistemological basis of content matter.
Further reading:
Self-Organization of Cognitive Performance
van Orden, Holden, & Turvey (2003)
Dynamics in cognition
Riley & Holden (2012)