Use CSS3 flex to lay out Files.app components.

ui/file_manager/file_manager/foreground/css/drive_welcome.css

 /* Copyright (c) 2012 The Chromium Authors. All rights reserved.
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file. */
 
 /* Google Drive welcome banners.*/
 .drive-welcome-wrapper {
   /* This image looks good in high DPI as is. */
   background-image: url(chrome://resources/images/clouds.png);
   background-repeat: repeat-x;
   color: #333;
 }
 
 .drive-welcome-icon {
   background-image: -webkit-image-set(
     url('../images/files/ui/drive_logo.png') 1x,
     url('../images/files/ui/2x/drive_logo.png') 2x);
   background-repeat: no-repeat;
 }
 
 .drive-welcome-links {
-  -webkit-box-orient: horizontal;
-  display: -webkit-box;
+  display: flex;
+  flex-direction: row;
 }
 
 .drive-welcome-button {
   -webkit-user-select: none;
   background-image: linear-gradient(to bottom, #f5f5f5, #f1f1f1);
   border: 1px solid rgba(0,0,0,0.1);
   border-radius: 2px;
   color: #444;
   cursor: default;
   display: inline-block;
@@ skipping 30 matching lines @@
 
 .drive-welcome-button.drive-welcome-start:hover {
   background-image:
     linear-gradient(to bottom, rgb(77, 144, 254), rgb(53, 122, 232));
   border-color: rgb(47, 91, 183);
   box-shadow: 0 1px 1px rgba(0,0,0,0.1);
 }
 
 /* Header welcome banner. */
 .drive-welcome.header {
-  -webkit-box-flex: 0;
+  flex: none;
   height: 100px;
   overflow: hidden;
   position: relative;
   transition: height 180ms ease, visibility 0 linear 180ms;
 }
 
 .dialog-container:not([drive-welcome='header']) .drive-welcome.header {
   height: 0;
   visibility: hidden;
 }
 
 .drive-welcome.header .drive-welcome-wrapper {
-  -webkit-box-orient: horizontal;
   background-size: 308px 100px;
   bottom: 0;
-  display: -webkit-box;
+  display: flex;
+  flex-direction: row;
   left: 0;
   position: absolute;
   right: 0;
   top: 0;
 }
 
 .drive-welcome.header .drive-welcome-icon {
   background-position: center 18px;
   background-size: 51px 44px;
   width: 120px;
 }
 
 .drive-welcome.header .drive-welcome-message {
-  -webkit-box-flex: 1;
-  -webkit-box-orient: vertical;
-  display: -webkit-box;
+  display: flex;
+  flex: auto;
+  flex-direction: column;
 }
 
 .drive-welcome.header .drive-welcome-title {
   font-size: 140%;
   margin-bottom: 4px;
   margin-top: 14px;
 }
 
 .drive-welcome.header .drive-welcome-text {
   margin-bottom: 6px;
 }
 
 .drive-welcome.header .drive-welcome-dismiss {
   display: none;
 }
 
 /* Full page welcome banner. */
 .drive-welcome.page {
   bottom: 0;
+  flex: none;
   left: 0;
   position: absolute;
   right: 0;
   top: 0;
 }
 
 .dialog-container:not([drive-welcome='page']) .drive-welcome.page {
   display: none;
 }
 
 .drive-welcome.page .cr-dialog-close {
   display: none;
 }
 
 .drive-welcome.page .drive-welcome-wrapper {
-  -webkit-box-align: center;
-  -webkit-box-orient: vertical;
+  align-items: center;
   background-size: 520px 173px;
   bottom: 0;
-  display: -webkit-box;
+  display: flex;
+  flex-direction: column;
   font-size: 120%;
   left: 0;
   overflow: hidden;
   position: absolute;
   right: 0;
   top: 0;
 }
 
 .drive-welcome.page .drive-welcome-icon {
   background-position: center center;
@@ skipping 24 matching lines @@
   margin-left: 20px;
 }
 
 body:not([type='full-page']) .drive-welcome.page .drive-welcome-wrapper {
   background-position: 0 0;
 }
 
 body:not([type='full-page']) .drive-welcome.page .drive-welcome-icon {
   height: 200px;
 }