Buddhism already has a strong process flavor, or so some people say. So what teachings might be good "entry points" for connecting to process thinking?
I have done Zen for 40 years. At the beginning of most services, we recite the bodhisattva's vow....three times, then go to Sutras, etc.
The many beings are without number. I vow to save them all
Greed, hatred, and anger abound, I vow to abandon them.
Dharma gates are without number, I vow to wake to them.
Buddha's way is without error, I vow to embrace it fully.
I found on Wikipedia another form that adds some more of the underlaying mystique
My own self I will place in Suchness, and, so that all the world might be helped, I will place all beings into Suchness, and I will lead to Nirvana the whole immeasurable world of beings.
The sutra further states that "with that intention should a Bodhisattva undertake all the exercises which bring about all the wholesome roots. But he should not boast about them."
The Heart Sutra is often considered the most accessible text, and also has a strong process flavor:
Form is emptiness, emptiness is form. Emptiness is not other than form, form is not other than emptiness. In the same way, feeling, perception, formation, and consciousness are emptiness. Thus, Shariputra, all dharmas are emptiness.