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I guess this means there won't be a design change for the new prices
Not necessarily true. Rumor has it that later in 2013 the USPS will issue another series of flag stamps (depicting the US Flag in four seasons).
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Does anybody know if the coil stamps are going to be reprinted as well?
I haven't heard. But remember these Four Flags Stamps were issued in several formats, including Booklets of 20, Booklets of 10, ATM Booklets of 18 and Coils of 100.
So far, I've only heard about the Booklets of 20 being reprinted. Since the Booklets of 20 were printed by two printers -- Ashton Potter (APU) and Sennett Security Products (SSP) there are likely reprints of both out there.
In fact, the original printing was for 1 billion stamps (50 million bookets) from each printer; it has been suggested that the reprints are of the same quantity ... so they will hardly be "rare", just adding another variety to collect.