Is my brother obligated to fast two months as expiation for accidental killing, knowing that he was 14 years old at the time of the incident, and the victim's family received the blood money?

What your brother committed, unintentional killing, necessitates the payment of blood money by his 'Aqilah (male relatives on the father's side) along with expiation. The expiation is to be performed in the following order: freeing a believing slave (which is now difficult to find), then fasting for two consecutive months. This is based on the verse: "And whoever kills a believer by mistake – then the freeing of a believing slave and a compensation payment presented to his family [is to be made] unless they [charitably] forgo it. But if he was from a people hostile to you and he was a believer, then the freeing of a believing slave [is sufficient]. And if he was from a people with whom you have a treaty, then a compensation payment presented to his family and the freeing of a believing slave. And whoever does not find [one or afford its price] – then a fast for two consecutive months as repentance to Allah. And Allah is ever Knowing and Wise." (An-Nisa: 92).

If your brother is an adult, he should fast for the expiation. If he is not an adult, then according to the Shafi'is, his fasting now, before puberty, is sufficient. However, the Malikis hold that his fasting now is not sufficient; rather, he must wait until he fasts after puberty.