I do this for the OS X build.
Just change the makefile to use the .a files of the libs instead of the .dylib files (and replace the sdl stuff with the output of "sdl-config --static (or --static-libs)).
You should be able to do it differently on linux by passing -static somewhere, but apple prevents that on OS X, so I can only give you the manual approach.
My patch to automate this for my build system (just to give you an idea, don't copy paste this):
everything that is -lfoo is a dynamic link, so you didn't replace those but added the static link
Example: -lfluidsynth needs to be *replaced* by /usr/lib/i386-linux-gnu/libfluidsynth.a
(though I'd try first with a lockstock Dosbox without any patch, like the fluidsynth one)
Also check the out pout of "sdl-config --libs" and replace that in the makefile with the output of sdl-config --static-libs
If anyone else is willing to help me with this,
I've uploaded the terminal output from my attempted compile here - https://ufile.io/bbe57
i though it'd be too large to post directly on these forums