An example of downloading a file and displaying progress with the LibGDX Net module.

Snippet.java

package com.badlogic.gdx.tests.lwjgl;

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;

import com.badlogic.gdx.ApplicationAdapter;
import com.badlogic.gdx.Gdx;
import com.badlogic.gdx.Net.HttpMethods;
import com.badlogic.gdx.Net.HttpRequest;
import com.badlogic.gdx.Net.HttpResponse;
import com.badlogic.gdx.Net.HttpResponseListener;
import com.badlogic.gdx.backends.lwjgl.LwjglApplication;
import com.badlogic.gdx.graphics.Color;
import com.badlogic.gdx.graphics.GL10;
import com.badlogic.gdx.scenes.scene2d.InputEvent;
import com.badlogic.gdx.scenes.scene2d.Stage;
import com.badlogic.gdx.scenes.scene2d.ui.Skin;
import com.badlogic.gdx.scenes.scene2d.ui.Table;
import com.badlogic.gdx.scenes.scene2d.ui.TextButton;
import com.badlogic.gdx.scenes.scene2d.utils.ClickListener;
import com.esotericsoftware.tablelayout.Value;

public class Snippet {
  
  public static void main (String[] args) {
	  
		new LwjglApplication(new ApplicationAdapter() {
			Stage stage;
			Skin skin;
			
			TextButton button;
			
			@Override
			public void create () {
				stage = new Stage(Gdx.graphics.getWidth(), Gdx.graphics.getHeight(), false);
				skin = new Skin(Gdx.files.internal("data/uiskin.json"));
				Gdx.input.setInputProcessor(stage);
				
				Table container = new Table();
				container.setFillParent(true);
				button = new TextButton("Click to download", skin);
				button.getStyle().disabled = skin.newDrawable("default-round", Color.DARK_GRAY);
				container.row();
				container.add(button).width(Value.percentWidth(0.50f));
				
				stage.addActor(container);
				
				button.addListener(new ClickListener() {
					@Override
					public void clicked (InputEvent event, float x, float y) {
						if (!button.isDisabled()) {
							button.setDisabled(true);
							
							// Make a GET request
							HttpRequest request = new HttpRequest(HttpMethods.GET);
							request.setTimeOut(2500);
							request.setUrl("http://libgdx.badlogicgames.com/nightlies/libgdx-nightly-latest.zip");
							
							// Send the request, listen for the response						
							Gdx.net.sendHttpRequest(request, new HttpResponseListener() {
								@Override
								public void handleHttpResponse (HttpResponse httpResponse) {
									// Determine how much we have to download
									long length = Long.parseLong(httpResponse.getHeader("Content-Length"));
	
									// We're going to download the file to external storage, create the streams
									InputStream is = httpResponse.getResultAsStream();
									OutputStream os = Gdx.files.external("libgdx-nightly-latest.zip").write(false);
									
									byte[] bytes = new byte[1024];
									int count = -1;
									long read = 0;
									try {
										// Keep reading bytes and storing them until there are no more.
										while ((count = is.read(bytes, 0, bytes.length)) != -1) {
											os.write(bytes, 0, count);
											read += count;
											
											// Update the UI with the download progress
											final int progress = ((int) (((double) read / (double) length) * 100));
											final String progressString = progress == 100 ? "Click to download" : progress + "%";
											
											// Since we are downloading on a background thread, post a runnable to touch ui											
											Gdx.app.postRunnable(new Runnable() {
												@Override
												public void run () {
													if (progress == 100) {
														button.setDisabled(false);
													}													
													button.setText(progressString);
												}
											});
										}
									} catch (IOException e) {
										
									}
								}
								@Override
								public void failed (Throwable t) {
									Gdx.app.postRunnable(new Runnable() {
										@Override
										public void run () {
											button.setText("Too bad. Download failed.");
										}
									});
								}
							});
						}
					}
				});
			}
			
			@Override
			public void render () {
				Gdx.gl.glClear(GL10.GL_COLOR_BUFFER_BIT);
				stage.act();
				stage.draw();
			}
			
		}, "Download Example", 480, 320, true);
	}
  
}

Thanks, this was very useful. Don't you need to close the OutputStream at the end?

Thanks, i wrote the downloading based on your solution