How can I let all my docker containers use my proxy?

See this SO answer:

Host server runs a container running a proxy (squid, in this case) that can do transparent proxying. That container has some iptables rules that NAT traffic into the proxy server - this means that container needs to run in privileged mode.

Host server also contains (and here's the magic) ip route table entries that re-route all traffic from any container but the proxy that was destined for port 80, through the proxy container.

That last bit essentially means that for port 80 traffic, the route from container to the rest of the world goes through the proxy container - giving it the chance to NAT and transparent proxy.

https://github.com/silarsis/docker-proxy

The Configure the Docker client official documentation shows how to easily solve this problem.

Edit the ~/.docker/config.json (or %USERPROFILE%\.docker\config.json) file and add the following JSON snippet:

{
    "proxies": {
        "default": {
            "httpProxy": "http://localhost:3128",
            "httpsProxy": "https://localhost:3128"
        }
    }
}

This solved my issue where running apt udpate inside a debian docker container would fail. After adding the proxy settings in that json file and starting a new docker container apt update started to work.