Is it correct to say, "Here's a for instance . . ."? (Meaning, "Here is an example")
I'm not sure how you would define "correct". But that is, indeed, a very common pragmatic usage in British and American speech--in my experience, especially in business contexts.
As I've never seen it written (even in reported speech), I'm not sure whether it is usually hyphenated or put in single scare quotes. But I would probably do one or the other to aid readers unfamiliar with your usage in disambiguating from the prevailing function of 'for example' as a sentence-modifying adjunct. Personally, I wouldn't write it except in reported speech, but I'm sure people do.
The usage is similar to saying "I do have a 'but' though" where 'but' refers to a caveat. in both cases, a phrase is being used as a placeholder for a description of its usual semantic function (or the class of things that would usually follow it). Syntactically, they are both functioning as a noun phrase despite being lexically another part of speech (an adverb and a conjunction, respectively).