Nope. I haven't had Fink installed at all, but thanks anyway. I get this error with both sqlite 2.8.15 and 3.0.8. Strange.
Try creating a new account and run configure within it. There may be something hosed in your environment or shell configuration.
Also, I have found that regenerating the configure script via 'autoconf' will often fix things (though I haven't had this specific problem with SQLite).
Note that the unit tests will fail when building a dynamic library on Mac OS X if TWOLEVEL_NAMESPACES is enabled. This is because of a bug in Makefile.in that effectively causes .o files to be linked multiple times in the testfixture binary.
b.bum