Flash is no longer being developed for Linux. The latest versions are only integrated with Chrome. If you're using Chromium, you can extract the Flash plugin from Chrome to use it separately. When using Firefox, you will need to switch to a different browser to access the latest versions. If you use Chrome and update to the latest version, installing this software is quite straightforward.
Steps
Installing on Chromium Browser

Open Ubuntu Software Center. You can access this from the Ubuntu toolbar.

Click Edit and choose Software Sources.

Click on "Ubuntu Software".

Check the box for "Software restricted by copyright or legal issues (multiverse)". Then click "Close".

Wait for the Software Center to update the sources. You may need to wait a few moments.

Search for "Pepper Flash Player". This will allow you to install the plugin for your browser.
- Although the package is named "pepperflashplugin-nonfree", it is actually free software.

Open the Terminal (Command Window). You can access the Terminal from the toolbar or press Ctrl+Alt+T.

Type .sudo update-pepperflashplugin-nonfree and press ↵ Enter.

Wait for the installation process to complete. You may have to wait a while. Once the process finishes, the computer's name will appear again. Enter exit and press ↵ Enter to close the Terminal.

Restart your browser. Flash is now installed for the Chromium browser.

Check for updates regularly. Once installed this way, Flash won't update automatically. You’ll need to manually check for new updates quite frequently.
- Open the Terminal.
- Type sudo update-pepperflashplugin-nonfree –status and press ↵ Enter to check for updates. If an available update shows a version number higher than the installed version, that means an update is available.
- Type sudo update-pepperflashplugin-nonfree –install and press ↵ Enter to install the update.
- Restart your browser to complete the update process.
Installation on Chrome Browser

Update your Chrome browser. Since Flash is built into Chrome, there's no need to worry about running the software. Just update Chrome to the latest version, and Flash will work as expected.
- If Flash is broken in Chrome, try uninstalling and reinstalling it.
Installation on Firefox Browser

Switch to Chrome or Chromium browser. Adobe no longer supports development for Linux except for the Pepper Flash plugin for Chrome. This means that the Flash plugin for Firefox is outdated, no longer improved, and only receives minor security patches.
- If you wish to install the outdated version for Firefox, continue reading.

Press CTRL + ALT + T simultaneously or press the "Super" (Windows) key and type "Terminal". Run the "Terminal". A terminal window will appear.

Type "sudo apt-get install flashplugin-installer"

Enter your sudo administrator password. You won't see any asterisks on the screen, but your input is still being registered.

Install the plugin by pressing "Y" (yes) in the Terminal.

Restart Firefox to activate the newly installed plugin.