The Lions overcame the Wallabies 23-21 in Brisbane last weekend to take the lead in the three-match series.
Bracken, who was part of the successful 1997 tour of South Africa, told Sports Mole that a number of injuries are likely to significantly hinder Australia's chances.
"While we've lost Paul O'Connell, I think we're going to go out there and annihilate them with their injuries," he said. "I see that happening in the next two Tests.
"The good thing is they've got the first win, players are coming back, they've got injuries, there's a South African referee who will referee the breakdown properly and I tell you what, they are going to get smashed. I think the Australians should look out."
The Lions go up against Australia in the second Test on Saturday when they two sides meet in Melbourne.
Rugby enthusiast Kyran Bracken has teamed up with Burger King to announce the return to 100% British and Irish beef with the re-launch of the Angus Collection. What better way to support our British and Irish Lions. The Angus Collection is now available in Burger King restaurants across the UK.