Since you didn't post the entire code it is difficult to determine the problem. I believe the issue lies in problem that your keyboard event is not firing. I would recommend trying the following code to see if it resolves your problem.
Instead of calling video10.clear();
I removed the object entirely as well.
import flash.events.MouseEvent;
import flash.events.KeyboardEvent;
import flash.net.NetConnection;
import flash.media.Video;
import flash.net.NetStream;
miguel_btn.addEventListener(MouseEvent.CLICK, video_miguel);
stage.addEventListener(KeyboardEvent.KEY_DOWN, handleKeyDown);
var video10:Video;
var display10:NetStream;
function video_miguel(event:MouseEvent):void {
display10 = new NetStream(new NetConnection());
display10.play("Miguel_1.flv");
video10 = new Video();
video10.attachNetStream(display10);
video10.x = 150;
video10.y = 250;
stage.addChild(video10);
}
function handleKeyDown(ke:KeyboardEvent):void {
//keycode 39 is the right arrow key.
if(ke.keyCode == 39) {
nextFrame();
//We can completely remove the video by calling the function below.
stage.removeChild(video10);
}
}