can you find key fragemnts from aram mathces?

I have yet to see a super duper clear answer on this matter. I have seen where people have claimed that it is possible, but have yet to see anyone actually get one in ARAM. My answer to you is unfortunately, I have no idea.

Edit: The clearest answer from Riot I have seen up to this point was in the Hextech Crafting introduction page thingy. This is where they said, "You can earn key fragments in any match made game". That quote is not exactly word for word but that is pretty much in the ball park.

Not yet. You can only gain Hextech Crafting materials through matches where you can gain champion Mastery. They'll be adding Champion Mastery to ARAM, TT, and the rotating game mode, and you'll be able to get your stuff there at that point.

http://www.surrenderat20.net/2016/03/red-post-collection-aurelion-sol_16.html#3

You can earn keys from any game mode or map that also grants Champion Mastery, if you don't earn Champion Mastery at the end of your game then you can't earn keys from it. However, they do plan to implement Champion Mastery into every map and game mode eventually, which will allow keys to also be earned as well.

thank you