I eat the food at home little by little so I don’t get caught
少しずつ - little by little, step by step
この場合はlittle by littleで大丈夫です
バレル - to get caught, to be caught
バレないように - so I don’t get caught
家にある食べ物 - the food we have at home, food at home
少しずつ取って食べてます - eat little by little, take a and eat little by little
I eat the food at home little by little so I don’t get caught