A task killer is not essential, however you can gracefully end processes that may be using up your Fire's memory. Whenever you exit out an App or touch the Home icon while in an App, the App goes into a suspend or hibernate state and is retained in memory. Also, many installed Apps like to conveniently start processes when your tablet starts (without you knowing it) eating up even more memory.
First, download a FREE App called Quick System Info Pro from the Amazon App Store. If you look under the Processes Tab of Quick System Info Pro you will likely see some Apps there that you launched and didn't launch stored in memory. If you are familiar with the App, touch it and select End Task. Only end processes you recognize. When you have ended all processes you recognize, select Quick System Info Pro from the processes list and end it.
Second, just like many PC programs, many installed Android Apps like to start themselves when your tablet starts. To limit the amount of Apps that "launch" processes at startup and conserve even more of your Fire's valuable resources, I recommend you download an App called Startup Cleaner 2.0 (Download Startup Cleaner here:
http://androiddev.orkitra.com/downlo...tartup2_v2.1.0 OR here
http://www.1mobile.com/startup-cleaner-2.0-97574.html). This App allows you to control which Apps you want to allow to "launch" at startup and which ones you don't. This helps conserve system resources as well as improve startup time.