It seemed I had everything but flex. I downloaded that and 
double-checked all of the dependencies. Everything compiles now but I'm 
getting a linking error.

I am using a CLEAN install of cygwin with the following packages:

setup -P 
cygwin,autoconf,automake,binutils,bison,bzip2,cygport,diffutils,fileutils,findutils,flex,gawk,gcc,git,libtool,make,patch,pkg-config,sed,tar,w32api,dri-drivers,libbz2_1,libfontenc1,libfreetype6,libgcc1,libGL1,libpixman1_0,libX11_6,libXau6,libXdmcp6,libXext6,xauth,xcursor-themes,xkbcomp,xkeyboard-config,zlib0,libdmx1,libXaw7,libXfixes3,libXi6,libXmu6,libXmuu1,libXrender1,libXt6,bigreqsproto,compositeproto,damageproto,dmxproto,fixesproto,font-util,fontsproto,glproto,inputproto,kbproto,libXfont-devel,randrproto,recordproto,renderproto,resourceproto,scrnsaverproto,windowswmproto,xcmiscproto,xextproto,xf86bigfontproto,xineramaproto,xorg-util-macros,xproto,xtrans,khronos-opengl-registry,libpixman1-devel,libx11-devel,libgl-devel,libxkbfile-devel,libxcb-image-devel,lib-icccm-devel,glapi-devel

Prepping, generating, and configuring:

cygport xorg-server.cygport prep
autogen.sh -V
configure

And on make I get the attached linker error. I've tried cleaning and 
redownloading twice now.

 > I think now might be an appropriate time to ask if you have all the
 > prerequisites listed in [1]?

Yes, I do. On that note, the prerequisites are missing:

libpixman1-devel
libx11-devel
libgl-devel
libxkbfile-devel
libxcb-image-devel
lib-icccm-devel

(detected during configure)

and

glapi-devel

(detected at compile-time)

There is also no sanity check for flex, although it is listed as a 
prerequisite.