I had this exact same problem on gentoo and ended up installing it with the gentoo package. I know if you download the actual source from www.imagemagick.org, you can get the magick/api.h from that source file and then use it to compile your code.
Godzirra! Destroying Neo Tokyo since 1954

In reply to Re: Image::Magick install failure - no magick/api.h by godzirra
in thread Image::Magick install failure - no magick/api.h by mikeraz

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