My washer water and sump pump water both go out into the same grey water tank. Recently the water has been backing up into the sump pump or washer depending on which one is being used. I dug up the well and found that the water is not draining due to sludge build up from soap and lint. The sludge is on the walls, in the drain spaces between bricks and covering the base of the well which is covered with small stones. This tank has been used for about 16 years without a problem. The water has been drained using a portable sump pump. I poured 2 bottles of chemical (can't remember what it was called) and 2 packets of this monthly flush stuff into the tank to try and eat up the sludge on the bottom of the tank but it does not seem to be going away. Is there something that I can use to get rid of the sludge? Any suggestions?

That much sludge will require that you dig it out. Furthermore, putting chemicals in the grey water will negate it's use since you wouldn't be able to recycle to plants etc.

Have it pumped just like a septic tank. Never use chemicals in a septic or gray water system.

Well for openers you can stop calling it a "gray water tank". You have a dry well. And they don't drain The water seeps through holes in the side and stones on the bottom.
I'm amazed it lasted for 16 years before clogging up. You're looking for a "Gee Whiz" product you can simply toss in there and get all that nasty smelly gook gone. Sorry! They don't exist. I am no fan of using harsh chemicals in a drainage. You have two options here:
1. Get down and dirty and clean the pipe and dry well out by hand, **OR**
2. Build a new dry well,(see image) in a different location,( The ground might be saturated with gunk after dumping sludge in it for 16 years.
Here's a little hint about how we got around sludge buildup back in the old days.
To prevent kitchen and washer gunk from going into out septic tanks and clogging up the drainfield we would install a grease trap ahead of the septic tank to trap the grease. Then all we had to do is lift the lid and clean out the grease trap and not the entire system just as you are facing. If it were me I'd go with door#2. Good luck, Tom