Not much study has been done on Pyrithione zinc during breastfeeding however it�s known to get absorbed in skin in some extant (Less than 1%). Topical usage is not likely to cause much problem but it�s suggested to search for safer alternative.
During whole lactation period you shall first discuss with your doctor and then together you shall decide whether you shall take that drug or not however if you have already taken Basic Essentials Dandruff Dry Scalp | Pyrithione Zinc Shampoo then you shall inform your doctor, But you should not be worried too much as Basic Essentials Dandruff Dry Scalp | Pyrithione Zinc Shampoo comes in category of low risk drug.
Basic Essentials Dandruff Dry Scalp | Pyrithione Zinc Shampoo comes in category of low risk and if your doctor is aware that you are breastfeeding it should be ok to use
Not much
US
National Womens Health and Breastfeeding Helpline: 800-994-9662 (TDD 888-220-5446) 9 a.m. and 6 p.m. ET, Monday through Friday
UK
National Breastfeeding Helpline: 0300-100-0212 9.30am to 9.30pm, daily
Association of Breastfeeding Mothers: 0300-330-5453
La Leche League: 0345-120-2918
The Breastfeeding Network supporter line in Bengali and Sylheti: 0300-456-2421
National Childbirth Trust (NCT): 0300-330-0700
Australia
National Breastfeeding Helpline: 1800-686-268 24 hours a day, 7 days a week
Canada
Telehealth Ontario for breastfeeding: 1-866-797-0000 24 hours a day, 7 days a week