Certainly. There is no way for the dye to get into your milk unless you consume or absorb the dye, in one way or another - and that's something you should never do in any case!
You should, of course, take the standard precautions when using dye - be careful not to breathe dust powder (wear a dust mask or respirator when measuring out dyes), wear gloves to prevent much skin exposure to the dye, and wash any spilled dye to make sure that none is inadvertantly consumed. Wear outer clothing that you can take off, or change your clothes, before feeding your baby, in case you've spilled dyes or soda ash on your clothing.
For more details, see also:
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