Going to go out on a limb here and say that the swal() function likely needs to be wrapped in a document ready function. Add console.log('test') to see that the method is actually being called.
This should come after the jquery script has been loaded. In my views, I typically add a @section('footer') // content @end and put all my js in there. Then in my master file, below my master js scripts (jquery, etc.), I'll render the footer section there. I.e. @yield('footer')
<script>
$(function() {
swal({
title: '{{ session("flash_message.title") }}',
text : '{{ session("flash_message.message") }}',
type : '{{ session("flash_message.type") }}',
timer: 1500,
showConfirmButton: false,
});
});
</script>