Keep BF as per normal, up her fluids even.

You will find that while they may share some illnesses you suffer, it isn't because of BM. But your antibodies to said illness will be in the millk.
So generally their bouts will be less severe than they could have been and will benefit from building their immunity - by both fighting the illness themselves and having your antibodies.

Hope that makes sense.
Esentially, whenever you or bubs (or both) are sick, the best thing you can do is to continue breastfeeding through the illness - BM is always better than any alternative in terms of health benefits when ill (save if you are taking some medication that is inappropriate for bubs)

Hope you both feel better soon!!