I'm while using following code to drag in Twitter Updates:

<?php

class TwitterFeed {
    public $tweets = array();
    public function __construct($user, $limit = 5) {
        $user = str_replace(' OR ', '%20OR%20', $user);
        $feed = curl_init('http://search.twitter.com/search.atom?q=from:'. $user .'&rpp='. $limit);
        curl_setopt($feed, CURLOPT_RETURNTRANSFER, true);
        curl_setopt($feed, CURLOPT_HEADER, 0);
        $xml = curl_exec($feed);
        curl_close($feed);
        $result = new SimpleXMLElement($xml);
        foreach($result->entry as $entry) {
            $tweet = new stdClass();
            $tweet->id = (string) $entry->id;
            $user = explode(' ', $entry->author->name);
            $tweet->user = (string) $user[0];
            $tweet->author = (string) substr($entry->author->name, strlen($user[0])+2, -1);
            $tweet->title = (string) $entry->title;
            $tweet->content = (string) $entry->content;
            $tweet->updated = (int) strtotime($entry->updated);
            $tweet->permalink = (string) $entry->link[0]->attributes()->href;
            $tweet->avatar = (string) $entry->link[1]->attributes()->href;
            array_push($this->tweets, $tweet);
        }
        unset($feed, $xml, $result, $tweet);
    }
    public function getTweets() { return $this->tweets; }
}
$feed = new TwitterFeed('trekradio', 4);
$tweets = $feed->getTweets();

?>

About this line: $feed = new TwitterFeed('trekradio', 4) - I wish to change "trekradio" therefore it pulls within the following value:

<?php if (have_posts()) { $flag = true;  while (have_posts()) { the_post();
if ($flag) { $value = get_cimyFieldValue(get_the_author_ID(), 'twitter-username');
if ($value != NULL) echo "<p><strong>Twitter: </strong> You can follow me on Twitter by <a href=\"http://www.twitter.com/" . cimy_uef_sanitize_content($value) . "\">clicking here!</a></p>";
$flag = false;    }}} ?>

How do i do that?

I am speculating that:

cimy_uef_sanitize_content(get_cimyFieldValue(1, 'twitter-username'))

is equivalent to 'trekradio'

If that's the case, use:

$feed = new TwitterFeed(cimy_uef_sanitize_content(get_cimyFieldValue(1, 'twitter-username')), 4);

Replace 'trekradio' with cimy_uef_sanitize_content(get_cimyFieldValue(1, 'twitter-username')).

Based on exactly what the cimy_uef_sanitize_content function does, maybe you simply need get_cimyFieldValue(1, 'twitter-username').