I'm never good with riddles, hence I only watch this thread.
crying
I know I could very well be wrong but trying wouldn't hurt. My answer is a broomstick.
Chealsea1368
Brown I am,
Long and slim,
I can fly,
Though in my owner's hands
Generally a broomstick's appearance and ability, and it only flies with its owners' hand.
Chelsea1386
I might happen to be,
The thing you see,
In someone's hands
Broomsticks could be seen in almost everyone's hands, especially in the Quidditich World Cups and Quidditch Teams.
Chelsea1386
You may touch me,
You may treat me carelessley,
Though I do not care
A broomstick is an object, and therefore cannot feel nor care on how they're treated.
Chelsea1386
I do not have an eye,
I can not ask for help,
The only thing I could do,
is fly.
A broomstick doesn't have an eye, obviously. The owner is the eye. It doesn't have a mouth so it cannot ask for help. And the only thing it could do was fly.
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I was thinking of wands before but I remembered that wands cannot fly on its own and have different colors, cores, woods, and length. So I chose broomsticks.
This is just a guess. I'm a loser with riddles. I can't even answer a relatively easy riddle.
crying 
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