Straight forward method:
Install Java and ZIP, Download & extract wallet and give execute permission to run.sh:
sudo apt-get install default-jre zip
wget https://github.com/burst-team/burstcoin/releases/download/1.2.8/burstcoin-1.2.8.zip
unzip -d ~/burstcoin-1.2.8/ burstcoin-1.2.8.zip
cd ~/burstcoin-1.2.8
chmod +x run.sh
Optional (download and extract updated BlockChain file) :
wget https://db.burst-team.us/db.zip && unzip -d ~/burstcoin-1.2.8/burst_db db.zip
Now start the wallet:
cd ~/burstcoin-1.2.8/
./run.sh