I hate to disagree with you, but I would tend to stay away from coffee and tea as dyes - as organic substances they will cause decay in the costume over time.
Are you using cotton or linen or a blend of both to make the shirt ? Those are the ideal materials for it. If you haven't made it yet, get a loose-ish weave linen and get it in a "natural", non-bleached state if you can (it will save you having to work from optic white - and hers was a "natural" colour to start with, too).
I would get a few (even just two) shades of fibre reactive dye to play around with. You can dilute a brown and send it through that dye bath a few times - it will be hot water and agitated, which will help age it a bit, too. That will give you an all-over mostly even filth coat. You can also lower the water level so it's not fully submerged, make it a bit less diluted and let it sit in and agitate less and only move it around a bit.
After that, I would use more concentrated dye on a brush or sponge - and work it into the fabric in areas that would be more dirty. I'd guess that the parts covered by the doublet-y thing are going to be slightly less filthy, for example. By working in that and using some of the dye in powder form crushed into it and THEN wetting it you'll get the look of dirty without having to use a substance that will degrade and decay over time.
During this, you can also wrap it around something you don't mind dirtying - like an old pillow, and having it fold how it would when you wear it under the other thing. That way you get realistic delineation of "filth" based on where it would be folded.
It's also possible to use dyes and such in an airbrush, but if you don't already have one it might now be worth it to you for just this.
If you want to get really into it, you can use a bath of VERY diluted bleach at this point and then repeat - so you'd get the effect of filth that someone tried to wash off at some point but then got filthy again.
I would also recommend after perhaps a few of the diluted washes letting it hang outside for a week or so - and hopefully it gets rained on and such.
Disclaimer : This post written by a Grumpy Old Man
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan