What does Kant think about non-corporeal, intelligent beings (i.e., angels)?
I can only answer here for his moral philosophy. If you need to ask about metaphysics and epistemology, I think the answer would be that he does not accept their existence as knowable -- but I don't recall reading anything specific on that point in Kant.
Kant does believe there are non-corporeal rational agents. And these would be bound by the categorical imperative. I say "bound", but it is a self-binding as a rational creature. Thus, they would share with humans the perfect duties that follow from the categorical imperative.
This holds true under all of the usual formulations of the categorical imperative and the text Religion within the Bounds of Reason Alone.
The reason is that the CI follows from pure reason and thus is the conclusion any rational being would draw (according to Kant). Thus, the universalizability test is not contingent on the fact we are embodied creatures but only on consistency with reason or consistency with reason and a world governed by the laws of nature.
Similarly, the second test regarding "humanity" does not mean homo sapiens humanity but rather is actually a synonym for rationality. Thus, always treat rationality where you encounter it as a being of worth not price (incomparably valuable) and never abuse such a being such that the being cannot apply its reason (i.e. don't lie to a rational creature).
The third set of formulas around autonomy and the realm of ends (or Kingdom of Ends) also say to act as if one is a rational creature in a country governed by rational law, which as Religion makes clear is, for Kant, not given from above by God but rather God validates the conclusions of this reason and God also performs the same deductions to reason to morality.
This account captures perfect duty and how that would apply to incorporeal rational beings for Kant -- they are bound just like we (as embodied rational creatures with desires that may distract us from morality) are to the categorical imperative and to maxims that could be universalized.
What such non-corporeal rational beings would not share with us is a commitment to the imperfect duties of self-improvement and helping others. The reason is the way in which embodied rational beings are held to this, viz., they come into existence in response to our own needs and inadequacies. I.e., at some point I obligated someone to help me, so I need to make this a sufficiently universal feature to have made my receipt of help moral and the only way to do that is to add a universal principle that requires me to sometimes help others.