Should breastfeeding parents be concerned about Zika?
According to the US Centers for Disease Control and Prevention:
To date, there are no reports of infants getting Zika virus through breastfeeding. Because of the benefits of breastfeeding, mothers are encouraged to breastfeed even in areas where Zika virus is found.“ 
Is it safe to use an insect repellent if I am pregnant or nursing?
Yes. Using an insect repellent is safe and effective. ” 
According to the World Health Organization:
Should pregnant women be concerned about Zika?
Health authorities are currently investigating a potential link between Zika virus in pregnant women and microcephaly in their babies. Until more is known, women who are pregnant or planning to become pregnant should take extra care to protect themselves from mosquito bites. If you are pregnant and suspect that you may have Zika virus disease, consult your doctor for close monitoring during your pregnancy.” 
What can I do to protect myself?
The best protection from Zika virus is preventing mosquito bites… This can be done by using insect repellent; wearing clothes (preferably light-coloured) that cover as much of the body as possible; using physical barriers such as screens, closed doors and windows; and sleeping under mosquito nets. It is also important to empty, clean or cover containers that can hold even small amounts of water such as buckets, flower pots or tyres, so that places where mosquitoes can breed are removed.” 
References & more information
1. Zika Virus Transmission, from the US Centers for Disease Control and Prevention
2. Question and Answers: Zika virus infection (Zika) and pregnancy, from the US Centers for Disease Control and Prevention
3. Zika virus disease: Questions and answers, from the World Health Organization
4. Breastfeeding in the context of Zika virus, Interim guidance, 25 February 2016, from the World Health Organization
Zika Virus Update from the InfantRisk Center
The Zika Virus and Breastfeeding by Miranda Gallegos, IBCLC
Zika Virus –Donor Milk from HMBANA milk banks is safe from Zika Virus from the Human Milk Banking Association of North America
Questions and Answers for Pediatric Healthcare Providers: Infants and Zika Virus Infection, from the US Centers for Disease Control and Prevention
Interim Guidelines for the Evaluation and Testing of Infants with Possible Congenital Zika Virus Infection — United States, 2016, from the US Centers for Disease Control and Prevention
Zika Virus Information, from the US Centers for Disease Control and Prevention
Zika Virus Information, from the World Health Organization
Zika Virus Transmission, from ZikaVirusNet.com
Zika Virus Infection, from the European Centre for Disease Prevention and Control