I have made some minor tweaks to make it more accessible as per earlier note.

http://jsfiddle.net/equinoxs/1x8w9c3n/1/

KeyHandler - should be able to use keyboard arrows if the focus is anywhere inside the slider
    _.$list.on('keydown.slick', _.keyHandler); //OLD
    _.$slider.on('keydown.slick', _.keyHandler); //NEW
To avoid the above inside the form fields.

        if(!event.target.tagName.match('TEXTAREA|INPUT|SELECT')) {  // NEW

          if (event.keyCode === 37 && _.options.accessibility === true) {
              _.changeSlide({
                  data: {
                      message: 'previous'
                  }
              });
          } else if (event.keyCode === 39 && _.options.accessibility === true) {
              _.changeSlide({
                  data: {
                      message: 'next'
                  }
              });
          }
      }
Removed the focus from the slider wrapper

      // if (_.options.accessibility === true) {
      //     _.$list.prop('tabIndex', 0);
      // }
Added the focus for the first focusable element inside the slide.

Updated the focus style.