To remove the blinking of symbolic links when doing ls in Linux:

LS_COLORS="ln=35" export LS_COLORS

That will set the ln=35 symbolic links to color purple.

Params for LS_COLORS:

di  Directory
fi  File
ln  Symbolic Link
pi  Fifo file
so  Socket file
bd  Block (buffered) special file
cd  Character (unbuffered) special file
or  Symbolic Link pointing to a non-existent file (orphan)
mi  Non-existent file pointed to by a symbolic link (visible when you type ls -l)
ex  File which is executable (ie. has 'x' set in permissions).

Another way is to edit ~/.dircolors and replace the 05 (blinking) for example:

ORPHAN  05;37;45
MISSING 05;37;45

Change to: