Merriam-Webster says about another the following:
being one more in addition to one or more of the same kind
However, I come across such sentences as: “I am giving another three books away”, “give me another 2 flowers”. I think it’s fine to say “give me another twenty minutes” as it is a period of time, but I wonder about “another two books/flowers”. Is it grammatically correct? Another thing which seems to be suspicious is that I can’t find such examples in dictionaries.
It is perfectly acceptable in any but the most formal contexts. It probably would not be used in legal or diplomatic texts, which must avoid any possible ambiguity, however far-fetched; but it’s fine in anything less restricted than that. Here, for instance, is a footnote from an impeccably academic text, Jon B. Sherman, The Magician in Medieval German Literature, University of Illinois at Urbana-Champaign, 2008:
Thorndike eventually continued his work, adding another three books that investigated the post medieval period up to the seventeenth century.
And it’s not a modern vulgarism, either. Here’s an extract from William Burt Harlow, An Introduction to Early English Literature, 1884, p.132:
By 1595 he had completed another three books of the “Faery Queen.”
(I should perhaps add that this use is not confined to threes of others—“another three” was my Google search term.)