Font and color checker chrome extension in JavaScript
Just some random comments from a quick read through:

1) Does this work if someone defines their colors using hex or name style (#fff, #ffffff, white, rgba(255,255,255,1)?

2) Walking the DOM and creating a huge array is probably not a good idea for anything but a small web page. After that you have another 3 separate loops. I would suggest that you create a function that walks the dom and calls a function for each node (function walkDom(start_element, callback) { .... Then you only need to store nodes that fail the test. Also combine ll those loops into one test.

3) Rather than comparing the nodetype with 1 I would use if (element.nodeType === Node.ELEMENT_NODE) ...

4) Rather than a do...while loop and nextSibling it is probably simpler just to get the childNodes and loop through them.

5) Or even better look into the TreeWalker api https://developer.mozilla.org/en-US/docs/Web/API/TreeWalker

6) This loop doesn't make sense:

for (elem in arr) {
  stylesContainer[arr[elem].tagName] = ...;
}


If you have two &lt;div&gt;'s in your tree the second one will over-write the first one.

7) A few things here:

if (brandColor.indexOf(stylesContainer[element]) &gt; -1) {
  //pass
} else if (document.querySelector(element).childNodes.length == 1) {
  document.getElementsByTagName(element)[0].style.border = "2px solid red";
  ...


}

Firstly don't use an if with an empty block, use a negated if :

if (brandColor.indexOf(stylesContainer[element]) &lt; 0 &amp;&amp;    document.querySelector(element).childNodes.length == 1) {


Also why only highlight elements with a single child and not those with two children or no children? Also consider using includes instead of indexOf And again this:

document.getElementsByTagName(element)


will return the first tag of that type in the document. It might not be the one with the issue. 

8) Don't mix styles. You use for ... in in some places and forEach in others. If you're using ES6 use let and const instead of var.

9) It is unnecessary to compare to true. if (fontNotMatch == true) { can be written as just if (fontNotMatch) {

10) If you check color you might want to check background-color and the various border-color's too.