The term "flush" is often mis-used.
Most places use a EXCHANGE machine, which connects into the transmission cooler lines.
They start the vehicle and let it idle, as the old fluid is pumped out by the pump INSIDE your transmission, the machine takes that fluid and replaces it with an equal amount of NEW fluid at the same rate that the old fluid is coming out.
THIS is completely safe.....no forcing fluid in or anything fancy.
You do NOT want and "cleaning" chemicals, just pure transmission fluid.
I expect your 2000 avalon calls for a Dexron III (often called Dex III) rated fluid, which is easy to find.
A synthetic would be best.
Read the bottle to see what specifications the fluid meets.
I would recommend that the transmission fluid be exchanged every 30K miles.
The filter in my 2003 Sienna is a nylon screen, does not do much filtering.
I installed a Magnefine filter in the transmission cooler line which provides filtration with a paper filter media (just like a mini oil filter cartridge) and also has a big magnet.
It has a pressure bypass that opens and lets the fluid bypass the filter media, should the media become clogged (unlikely when used as recommended).
They recommend that the Magnefine filter be changed once a year.
Here is a link to the first in a series of pictures that show the transmission fluid exchange, including removal of the pan and replacement of the filter (strainer).
http://rides.webshots.com/photo/2777272300011220610kWfEeM
Because I am using the Magnefine filter and plan to change my ATF EVERY year, I plan to remove the pan and replace the filter every OTHER year.
If you look forward through the pictures, you will see how I changed the power steering fluid, which uses the SAME Dexron III rated fluid as the transmission.