wanna run but afraid of becoming flatter

The only situation in which running would cause you to get a bit flatter would be if you started running regularly but didn't increase your calorie intake a bit, and then you might possibly lose some weight, possibly around your chest. However it is not a guarantee and if you make sure to eat enough, it won't cause that - there's no direct correlation between running and flatter chest, just if you lose weight you could potentially lose some fat there. I wouldn't worry about it if you're just planning on running once a week or something like that, you'll be perfectly fine!

My suggestion is, start doing yoga because as said you are mega skinny and flat, that’s why yoga is the best option for you, it will increase your eating efficiency. After you gain good weight then try running.