How to synchronize with the bitcoin blockchain via bitcoinJ
So I think I found the solution to my own question after looking around a bit.

I modified the constructor to explicitly set the peer addresses, like this:

public SimpleExample() throws UnknownHostException {

        walletAppKit = new WalletAppKit(NETWORK_PARAMETERS,DIRECTORY, "test");
        walletAppKit
                .setAutoSave(true)
                .setBlockingStartup(false)
                .setPeerNodes(//Seed nodes for the test network
//                        new PeerAddress(InetAddress.getByName("seed.bitcoin.sipa.be"), 18333),
                        new PeerAddress(InetAddress.getByName("testnet-seed.bitcoin.petertodd.org"), 18333),
                        new PeerAddress(InetAddress.getByName("node3.mycelium.com"), 18333),
                        new PeerAddress(InetAddress.getLocalHost(), 18333));
    }


Another thing I did was to call 2 methods on the WalletAppKit to start the synchronisation:

walletAppKit.startAsync();
walletAppKit.awaitRunning();