Nowadays, blockchain technology is seen as one of the main technological innovations to emerge since the advent of the internet. Many applications can benefit from blockchain to protect their exchanges. Nonetheless, applications with more restricted interests cannot use public blockchains. Permissioned blockchains promise to combine effectiveness of blockchains with stricter permissions to join blockchain's network. In permissioned blockchain, the number of participating entities is limited compared to public blockchain. However, by targeting the peers of the blockchain, the attackers can easily take control of consensus process and halt the blockchain operations. In this paper, we propose BrainChain, a scalable and efficient scheme to protect permissioned blockchain nodes from the largest ever Distributed Denial of Service (DDoS) attack (i.e., Domain Name System (DNS) amplification attack) in the context of software defined networks (SDN). BrainChain consists of 4 schemes: (1) Flow statistics collection scheme (FS) to gather the features of flows in an efficient way using sFlow; (2) Entropy based scheme (ES) to measure disorder of network features; (3) Bayes Network based Filtering scheme (BF) to classify, based on entropy values, illegitimate DNS requests; and (4) DNS Mitigation (DM) scheme to mitigate in an effective way the illegitimate flows (i.e., illegitimate DNS requests). Experimental results show that BrainChain can quickly and effectively detect and mitigate the attacks (i.e., DNS amplification attacks) with a high accuracy and a small false positive rate making it a promising scheme to protect blockchain applications from DNS Amplification attacks.