I'll also add that ngram isn't really accurate for older books in general. If you dig further in the search results, you'll see that Google is picking up a lot of words that aren't actually iron, Latin "non" being a key offender. (It does this for the other periods as well, but it's worth keeping in mind the tool's limits for historical research.)

That said, the term "Iron Age" was definitely in vogue in 17th century England to label the contemporary era (in constrast with earlier Golden, Silver, Brazen Ages). Thus Margaret Cavendish in Animal Parliament, "hard Iron of strong Judgement's fit for use, in Peace or Warr, to joyn up Errors loose." (In the introduction she refers explicitly to her book being published in an Iron Age.) But this use isn't specific to a narrow five-year period by any means. Thomas Heywood starts his series of "Age" plays around 1610.

There are a number of entries in Google Books for Dudley's Metallum Martis, or, Iron made with pit-coale, sea-coale ... published that year, as well as some discussion of it in journals that are digitized. It looks like it's a fluke of publication and possible multiple counting of a book published in a certain year and multiply digitized or indexed. Add to that the relative paucity of works attributed directly to 1665 and you get the 0.1% incidence (not really overwhelming, despite the ngram view) of works with "iron."