I ran into problems trying to do build in a separate build directory which I do by default i.e. not in the same directory as source is located. It looks like the include directories and source locations need to be prefixed with $(top_srcdir) in the Makefile.am(s).
mkdir build; cd build;
ln -sfn . $(top_srcdir)/proxy/api/include/ts
$(CC) $(CFLAGS) -I$(API_INC) -o add-header.o -c $(top_srcdir)/example/add-header/add-header.c