I am designing an cycle fixture for dust and grass testing our parts. The bottom plate of the fixture has an 0.5" thick aluminum plate that has 299 0.093" diameter holes on 1" square centers. The holes are for air to come up through to evenly blow the debris. I have a chamber mounted under this plate that has inside deminsions of 22.25"x 13.5" x 3". I would like to mount a blower fan to this chamber to force equal air though all 299 holes in the cycle test fixture. What would be the best way to determine the CFM needed to accomplish this and to properly size the fan.  

Not enough information. What is the velocity you want?
You will never get equal flow through all your holes.

Google "pressure drop perforated plate" to get a feel for what you need to know to even begin to approach the problem.

Note however that most of what you will find deals with "thin plates".  Your tiny holes in 1/2" thick plate don't qualify.

I think because of the thickness of your plate, you will have to solve the pressure drop and friction for a tube .093" dia and half an inch long, then add the results for the other 299.
 For what you are trying to do, you are creating a plenum chamber under the aluminum plate. Ideally you would want that chamber to be deep enough to to allow your air to stabilize out so that turbulence and swirl from the fan do not affect your air distribution. The 3" dimension you have now may not be enough.
B.E.

The good engineer does not need to memorize every formula; he just needs to know where he can find them when he needs them.  Old professor