Yes it's OK and very safe to breastfeed while the mother is sick with the flu, cold etc.
The baby cannot get any sickness such as the flu, cold or other virus through the breast milk.
The flu and cold viruses do not infect the breast milk so the baby cannot get sick through breastfeeding.
So if you're breastfeeding and feel good enough to allow your baby to breastfeed then continue to do so as the baby will be perfectly fine.
The baby might still catch a cold or flu from being in contact with you but they would catch the flu or cold virus from you anyway.
Because when you have a baby you cannot avoid touching or handling them when you're sick.
Your breast milk actually contains good antibodies which can help prevent sickness in the baby so it's a good idea to breastfeed even when you're sick.