Well, I totally get where your family is coming from. The US government has a history of being very violent towards tribes and Native communities, including when it comes to medicine and health care.
What you can say to your family to explain the flu shot is that this year especially it is important to get flu shots because it helps protect you and your loved ones from the flu, and it also helps to lessen the burden of the flu on providers, clinics, and public health staff who are also responding to COVID-19 in their communities.
To learn more about the flu vaccine go to this page: What are the benefits of flu vaccination?
To find out where to get a flu shot, go to Vaccine Finder.
I hope this helps and stay safe