Yes, we do have herd immunity to the common flu. It's why, for most people with healthy immune systems, the flu is a real annoyance, but nothing more. For those with compromised immune systems, such as AIDs patients, the old, and the very young, the flu can be a disaster. But, once a young child gets the flu a few times, they develop herd immunity so that subsequent infections are less severe.

Once in a while a flu virus learns to trigger the immune system of those with immunity to flu viruses, and then flu pandemics happen, but that is a rare occurence relatively speaking.