I wouldn't bother dying anything - TBH the few times I've tried, I've been considerably underwhelmed by the results...
You could just shred some old clothes, or get some from charity shops to shred, and tie the strips to netting.
I've got a big piece of net that seems to have been made for securing cargo or something like that (it's got a wide edge strip with inch wide brass eyelets but it's only about 1/2 inch squares so perfect for the job). I have a vague plan to use it with shredded clothes and garden twine - you can get that in tan and green. I think I'm going to try to get some plastic/cloth foliage too...