I have included LINKTYPE => 'static' in Makefile.PL

Did you do that for *both* of the Makefile.PL files - ie the one in the Expat folder as well ?
Like Anonymous Monk, I'm thinking that this approach might have serious problems, but I've absolutely no experience to back up that expectation ... and I notice that the error is in relation to an XML::Parser::Expat function, not XML::Parser.

AFTERTHOUGHT: looks like XML::Parser itself might be pure perl, which might make the LINKTYPE setting relevant only for the Expat/Makefile.PL ... which, I'm now guessing, you've already done.

Cheers,
Rob