Ken, all of the various types of flo-jet B&S carburetor do not have a float level specified in the manual - the only specifications are that the seat must be pressed into the top of the body until level with the surrounding metal, and the float must be parallel to the top of the body when the needle is closed.
Float level will not be the problem if the engine starts then stops. It is just about certain to be either ignition or fuel supply, and fuel is more likely than ignition if this happens consistently each time you start it and it never misfires or runs on one cylinder. If you disconnect the fuel hose from the carburetor, turn on the fuel tap and let the fuel flow from the hose into a jar, does it flow steadily? If not there is an obstruction in the tank, or the tank is empty. If it passes that test, and if the passage from the fuel hose barb through the needle and seat is not blocked with gunk, it is heading toward being an unusual case.
What setting are you using for the main jet adjustment? Since you have dismantled and reassembled everything, it may require resetting to the starting point and re-tuning. And can we have a picture of the carburetor please, so we will know which model it is?
Last edited by grumpy; 12/11/10 06:18 AM.