icons.js

console.log("-----------------------------");

document.querySelectorAll('link[rel="icon"]').forEach(
    function(currentValue, currentIndex, listObj) {
        console.log("ICON (" + currentValue.sizes + "): " + currentValue.href)
})

document.querySelectorAll('link[rel="shortcut icon"]').forEach(
    function(currentValue, currentIndex, listObj) {
        console.log("SHORTCUT ICON (" + currentValue.sizes + "): " + currentValue.href)
})

manifest.json

{
  "manifest_version": 2,
  "name": "Mozilla Android Components - Browser Icons",
  "version": "1.0",
  "content_scripts": [
    {
      "matches": ["*://*/*"],
      "js": ["icons.js"],
      "run_at": "document_end"
    }
  ]
}