Er ist ein postdoc Forscher in/für Philosophie.
Does it require "ein"? Should it be Postdoc-Forscher or separate? And should I use in or für?
I may not be doing philosophy, but I describe myself and my job as:
Ich bin Postdoc (in Chemie) an der Uni Kyoto.
You can also use arbeiten als but contrary to the other answer I would not say *einen Postdoc machen because it is a job, not a title I wish to ultimately gain. (I did say Ich mache meinen Doktor at my previous university; for the job, the job title Doktorand exists.)
(It was pointed out that there are other things such as ein FSJ, ein Praktikum that would be usable with machen. Those things are countable; even though I am on my second postdoc position I wouldn’t say that this is my *zweiter Postdoc. There is only one postdoc phase but it can be made up of multiple positions at different universities.)
As for the ein, if you wish to imply he is one of many then it should be there. If you are just stating his profession then it would usually be left out.
Hardly anybody would say Postdoc-Forscher or Postdocforscher (a space would be wrong; putting a space in noun compounds in German is condescendingly called a Deppenleerzeichen). These aren’t technically wrong they’re just overspecified as a postdoc is already a researcher. In English, the construction postdoctoral researcher exists which doesn’t have a direct parallel equivalent in German as far as I am aware.
As mentioned in the comments, you can say
Er ist Postdoc in Philosophie
Although to me it sounds more natural to say
Er macht seinen Postdoc in Philosophie
Or a bit more formal:
Er absolviert seinen Postdoc in Philosophie.
An independent postdoctoral researcher would be:
Er ist ein unabhängiger Postdoc in Philosophie.