The package system for PCLinuxOS is Synaptic. It's already included. Don't be fooled by the name. This version of Synaptic processes rpms. All the packages in the PCLinuxOS repositories are rpms.
Look in the Software Center section of the menu. If there's an Update Package Sources List entry, run that first. It will poll all the repositories and find the fastest one in relation to where you are. Please heed the advice and do not use the ibiblio.org repository.
Next, start Synaptic Package Manager. The icon may be on your desktop or in a toolbar somewhere. It varies by what desktop you're using. You can easily find it in the Software Center section of the menu. After starting, click the big Reload button in the upper left corner. That will update the package list. Next, click the Mark All Upgrades button. Once they've been marked, click the Apply button. In the dialog window that comes up, press Apply again. Packages will be downloaded and installed, including any dependencies.
After doing that, you can use the large Search button to find what you're looking for. In this case, enter the term flash. I believe you're looking for the web browser package, which is flash-player-plugin. It was probably already installed and upgraded in the previous steps. However, if it's not installed, just left-click the box to the left of the package name and mark it for installation. Then click the big Apply button again. Click Apply, once more, in the dialog window that appears.