Do the moths during Grumman's thoughts have any symbolic significance? In episode 47 (12:08) of Fullmetal Alchemist: Brotherhood, general Grumman's thoughts about a leadership position in Central are made audible to the viewer:

Miles: And what about the plan, sir? Aren't you going to proceed to central?
Grumman: I don't seem to have much choice. I suppose I'll just have to let Colonel Mustang have the biggest slice of Central pie.
Grumman (thinking): Bradley's current administration will still be properly functioning at this point in time. If Colonel Mustang or General Armstrong try to make their move now, every soldier in Central will be ordered to retrieve their treasonous heads. And once they're captured, I'll step in to restore order. They'll take the fall as enemies of the state, while General Grumman will heroically come riding in on a white horse. I'll let the youngsters dive head-first into danger and do all the dirty work, and then I'll take my rightful place as leader of this country without any risk.

During the bolded part of his speech above, a lamp is shown with a few insects—which appear to be moths—hovering around it. One unfortunate insect flies into the lamp and is burned to death.

This seems like an odd thing to show during such a speech, which leads me to believe it might have a deeper meaning. Does this lamp scenario or the moth's death symbolize anything?
I believe this refers to the saying "like a moth to a flame".

The saying indicates that something/someone is irresistibly attractive (not necessarily as in human attraction), but that it will ultimately lead to downfall. Remember, at the end, the flame engulfs the moth, and it dies.

So, Bradley and Mustang are fighting for peace/freedom/a good future. They themselves believe that they cannot stay away from the fight, as it must be done in order to achieve their goals. Yet still, the path they take is being predicted and taken advantage of, which, in the eyes of Grumman, will lead to their downfall.

So, the metaphor with the moth is used in a perfectly valid manner.