gistfile1.html

  <!-- iPhone 6 Plus -->
  <link href="startup-image-1242x2148.png"
    media="(device-width: 414px) and (device-height: 736px)
      and (-webkit-device-pixel-ratio: 3)"
    rel="apple-touch-startup-image">

gistfile2.rb

# generate startup images for all known iOS combinations

SIZES = %w(
  1242x2208|60|retina-5_5|iPhone_6_Plus
  750x1334|40|retina-4_7|iPhone_6
  640x1136|40|retina-5|iPhone_5
  640x960|40|retina|iPhone_4
  320x480|20|iphone|iPhone

  1536x2048|40|ipad-landscape-retina|iPad_Retina
  1536x2048|40|ipad-portrait-retina|iPad_Retina
  768x1024|20|ipad-landscape|iPad
  768x1024|20|ipad-portrait|iPad
)

SIZES.each do |size|
  res, statusbar, name, device = size.split('|')
  w, h = res.split('x').map(&:to_i)
  h -= statusbar.to_i
  `convert -size #{w}x#{h} xc:blue -pointsize 36 -fill white -draw "text 25,50 '#{w}×#{h}: #{name}'" -draw "text 25,90 '#{device}'" -draw "circle #{w/2},#{h/2} #{w/2},#{w/2}" startup-image-#{w}x#{h}.png`
end

Startup images on iOS web apps need to be cut to not include the status bar area. Due to a bug in iOS that's been around since iOS 7, the image is vertically streched when the app is starting up (I can't find how to make that stop). For the @3x Retina HD screen on an iPhone 6 you thus need an image that is 60 pixels shorter than the (virtual) screen resolution, which amounts to 1242x2148.

matchMedia('(device-width: 414px) and (device-height: 736px) and (-webkit-device-pixel-ratio: 3)').matches
// => true on iPhone 6 Plus

For completeness, here's the HTML for the same thing on iPhone 6:

  <!-- iPhone 6 -->
  <link href="startup-image-750x1294.png"
    media="(device-width: 375px) and (device-height: 667px)
      and (-webkit-device-pixel-ratio: 2)"
    rel="apple-touch-startup-image">

If you want to be complete, there's also the iPhone 6 Plus in Zoom mode: same logical-pixels dimensions as the iPhone 6, but a device-pixel-ratio of 3 (so your picture would have (375*3)x(667*3-60) = 1125x1941).