This is another Biblical reference. It comes from Isaiah 44:20, which reads: “He feedeth on ashes: a deceived heart hath turned him aside, that he cannot deliver his soul, nor say, Is there not a lie in my right hand?”
The phrase refers to food that tastes awful, obviously; it tends to be used in a context where someone has triumphed, but the victory is hollow. Major Major is of course not pleased at all by all the finery that Milo has placed at his disposal, because he hates to stand out from everyone else.
Interestingly, President Kennedy would employ the phrase in a radio speech during the Cuban missile crisis, less than a year after Catch-22 was published: “We will not prematurely or unnecessarily risk the costs of a worldwide nuclear war in which even the fruits of victory would be ashes in our mouth — but neither shall we shrink from that risk any time it must be faced.”