As you can see, there are a lot of duplicated -lz, -lm and others, so I doubt that libmysqclient is an exception and can't be used twice.
So, where the error message?
Also, please describe the software used in the build system.

Right, I don't know why the duplication of -lmysqlclient causes problems.

But I get about 80 pages of this:

/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x0): multiple definition of `net_buffer_length'
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x0): first defined here
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x4): multiple definition of `max_allowed_packet'
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x4): first defined here
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x8): multiple definition of `net_read_timeout'
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0x8): first defined here
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0xc): multiple definition of `net_write_timeout'
/usr/lib/mysql/libmysqlclient.a(libmysql.o)(.data+0xc): first defined here

Nothing weird in my build tools, they should all be the standard stuff that comes with FC2.
gcc 3.3.3 20040412
GNU Make 3.80

The only thing not stock involved is MySQL 4.1.11 installed from RPMs on the mysql website.

It's caused most likely by the fact that mnogosearch uses also mysql libs -> you need to link PHP with the SAME libs:
Use: --with-mysql=/usr