pagination for list category posts ( Custom post type )

Update you code with this

<?php // Output all Taxonomies names with their respective items
        $catCount = 0;
        $terms = get_terms('sermon-series');
        foreach( $terms as $term ):
        ?>                          
            <div class="sermon_title_area">
                <h3><?php echo $term->name; // Print the term name ?></h3>   
                <div class="sermon_date">
                    <p><?php echo $term->description; ?></p>
                </div>
            </div>
            <div class="flexslider carousel">
                <ul class="slides"> 
              <?php                         
                  $posts = get_posts(array(
                    'post_type' => 'sermon',
                    'taxonomy' => $term->taxonomy,
                    'term' => $term->slug,                                  
                    'nopaging' => true, // to show all posts in this taxonomy, could also use 'numberposts' => -1 instead
                  ));
                  foreach($posts as $post): // begin cycle through posts of this taxonmy
                    setup_postdata($post); //set up post data for use in the loop (enables the_title(), etc without specifying a post ID)
              ?>    

                <li>
                    <div class="slider_contents">
                        <a href="http://www.youtube.com/watch?v=<?php echo get_field('youtube_video_link'); ; ?>" rel="prettyPhoto" title="<?php the_title(); ?>"><?php the_post_thumbnail('slide-image', array('class' => 'slide-thumb')); ?></a>
                        <div class="slider_inside">
                            <h2><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
                            <div class="date">
                                <?php the_time('F j, Y'); ?>
                            </div>
                            <div class="excerpt_contents">
                                <?php echo excerpt('10'); ?>
                            </div>
                            <?php if ( get_field('mp3_link') ) : ?>
                            <div class="download_link">
                                <a target="_blank" href="<?php echo get_field('mp3_link'); ?>">Get the MP3 >></a>
                            </div>
                            <?php else : ?>
                            <?php endif; ?>
                        </div>
                    </div>
                </li>     
                <?php endforeach; ?>
                </ul>
            </div>                  
        <?php 
        $catCount++;
        if($catCount == 2)
        {
            echo '<a href="'.get_term_link($terms{2}->term_id, $term->taxonomy).'">Next</a>';
        }
        endforeach; ?>