How to download Ubuntu updates to a flash drive, and use it to update other PCs?

Try the apt-offline package:

Description: offline APT package manager

apt-offline is an Offline APT Package Manager.

apt-offline can fully update and upgrade an APT based distribution without connecting to the network, all of it transparent to APT.

apt-offline can be used to generate a signature on a machine (with no network). This signature contains all download information required for the APT database system. This signature file can be used on another machine connected to the internet (which need not be a Debian box and can even be running windows) to download the updates. The downloaded data will contain all updates in a format understood by APT and this data can be used by apt-offline to update the non-networked machine.

apt-offline can also fetch bug reports and make them available offline.

• Here's an example of shell usage. It's easy to learn. From the same page, here is how to use it:

Using apt-offline:

You generate a signature on your Debian box at home and carry the signature file on a removable medium (Probably a USB Stick).(e.g. "apt-offline set /tmp/apt-offline.txt")

Now you take the USB Stick (with the apt-offline.txt signature file) to the office machine which could be running any linux version, or as I mentioned above, even Windows.

There, you could run apt-offline giving it the signature file. (e.g. "apt-offline get C:apt-offline.txt")

apt-offline would generate you an archive file or a folder with all the data.

That data can be copied on a removable media. The removable media can be attached back to the disconnected Debian box at home and installed. (e.g. "apt-offline install /tmp/apt-offline.zip")

• Here's the manpage

...or you can make things SUPER-easy with the apt-offline-gui package.

This package contains the graphical user interface to apt-offline.