the styles it is using are more specific than the ones you're trying to override them with.
To remove completely:
#featured-slider .flex-direction-nav { display:none; }
then you'll need to remove the padding from #featured-slider
:
#featured-slider { padding:none; }
if you're testing in firebug you will need to scroll once you add these styles for the plugin's jquery to show the adjustments correctly.
To re-size:
you need to adjust the width of the next/prev slides, the width of the link, the positioning of the arrows, and the positioning of the circles around the arrows. example of 100px wide:
<!-- next/prev slide width -->
#featured-slider { padding-left:100px; padding-right:100px; }
<!-- link width -->
#featured-slider .flex-direction-nav a { width:100px; }
<!-- circle position -->
#featured-slider .flex-direction-nav a:after { left:30px; }
<!-- arrow position -->
#featured-slider .flex-direction-nav a:before { left:36px; }
hope that helps.