Suppose a boss is telling his/her subordinates not to be angry by saying 怒らないでおくれよ。
What is the meaning of おくれ in this context? And is it interchangeable with the sentence "怒らないでくれよ。" ?
「Verb in て/で Form + おくれ」
is rarely used in real life these days. That is unless there are regions where it is still used frequently that I am not aware of.
I have lived half of my life in Tokyo and the other half in Nagoya, but I cannot say that I have heard 「~~て/で + おくれ」 with any kind of consistency around those two cities.
Where do I see/hear it? Mostly in fiction, to be honest. Children's stories, song lyrics, period dramas, etc. Every single native speaker would remember hearing it as a kid said by older characters in children's stories.
The above is why it is difficult to answer your question "Are おくれ and くれ interchangeable?" In meaning, yes, certainly, but we just do not use the former. We mostly just use the latter (or the politer form 「ください」).
As far as pure meaning, however, the two sentences below mean the same thing:
「[怒]{おこ}らないでおくれよ。」
「怒らないでくれよ。」
= "Don't get angry!"
Yes, they are interchangeable, and we usually use してくれ now.
About this おくれ, it has two opinions. One is お in おくれ is 美化語 like お食べ and another is おくれなさい omitted なさい.
And it is a dialect of Wakayama prefecture. http://www.weblio.jp/content/%E3%81%97%E3%81%A6%E3%81%8A%E3%81%8F%E3%82%8C