I just developed a considerably easier solution. (Yes, I know this is an old question but someone researching this same issue may find this useful.)
I was using an SVG called hamburger.svg. I looked at it with a text editor and couldn't find anything that was setting a colour for the three lines - I'm guessing it defaults to black because that's certainly the behaviour I get - so I simply added a "stroke" parameter to the definition of the SVG. That didn't QUITE work - the borders of the three lines were my chosen colour (white) but the rest of the line was still black so I added a "fill" parameter as well. And that did the trick!
Here is the code for the original hamburger.svg in its entirety:
<?xml version="1.0" ?><!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN' 'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'><svg height="32px" id="Layer_1" style="enable-background:new 0 0 32 32;" version="1.1" viewBox="0 0 32 32" width="32px" xml:space="preserve" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M4,10h24c1.104,0,2-0.896,2-2s-0.896-2-2-2H4C2.896,6,2,6.896,2,8S2.896,10,4,10z M28,14H4c-1.104,0-2,0.896-2,2 s0.896,2,2,2h24c1.104,0,2-0.896,2-2S29.104,14,28,14z M28,22H4c-1.104,0-2,0.896-2,2s0.896,2,2,2h24c1.104,0,2-0.896,2-2 S29.104,22,28,22z"/></svg>
And here is the code for the new SVG after I edited it and saved it as hamburger_white.svg:
<?xml version="1.0" ?><!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN' 'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'><svg height="32px" id="Layer_1" style="enable-background:new 0 0 32 32;" version="1.1" viewBox="0 0 32 32" width="32px" xml:space="preserve" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><path d="M4,10h24c1.104,0,2-0.896,2-2s-0.896-2-2-2H4C2.896,6,2,6.896,2,8S2.896,10,4,10z M28,14H4c-1.104,0-2,0.896-2,2 s0.896,2,2,2h24c1.104,0,2-0.896,2-2S29.104,14,28,14z M28,22H4c-1.104,0-2,0.896-2,2s0.896,2,2,2h24c1.104,0,2-0.896,2-2 S29.104,22,28,22z" stroke="white" fill="white"/></svg>
As you can see if you scroll way over to the right, all I did was add:
stroke="white" fill="white"
to the very end of the path. The other thing I had to do was change the file name of the hamburger in the HTML. No messing with the CSS at all and no need to track down another icon.
Easy-peasey! You can imitate this to make your hamburger any colour you like.