This can be done through internal thoughts. Show what your character thinks about their situation and what has led to it. That should reveal some insights as to the world he/she comes from. For example:-
She threw the cup at the wall and watched it smash. Bloody government. I've already voted once. Why have I got to do it again?
That reveals at once that the government is dictatorial, voting is clearly compulsory, and any world where you have to vote again (to get it right this time perhaps?) is somewhere you probably don't want to live if you have the choice. She is taking her frustration out on a cup so there is no choice element here (and almost certainly severe consequences if she doesn't vote again).
You can also show something of your created world through what your character observes. In a flash fiction story, this would have to be a line or two at most (though that does make you stick to the really important things you want your reader to know so is no bad thing).
Description is the obvious way of showing a world but, again, in flash, a line or two at most and focus on what is important to the character (as this also reveals a lot about them).