Where should my method(s) that connect to DynamoDB go?

I would suggest adding a new package Infrastructure that contains all the configurations and connections for all your database/caching/messaging systems.

Infrastructure
    \DynamoConnection.java
    \DynamoConfiguration.java
    \IDynamoConnection.java
    \IDynamoConfiguration.java        

The credentials should be managed by a DynamoConfiguration class that reads from a configuration file.

The connection itself should be managed by a DynamoConnection class that accepts a DynamoConfiguration as a parameter and builds the connection during the object initialization.

public class DynamoConnection implements IDynamoConnection {

    private final AmazonDynamoDB connection;
    private final DynamoConfiguration config;

    public DynamoConnection(DynamoConfiguration config) {
        this.config = config;
        this.connection = AmazonDynamoDBClientBuilder.standard()
            .withRegion(this.config.region())
            .withCredentials(this.config.credentials())
            .withClientConfiguration(this.config.clientConfiguration())
            .build();
    }

    public AmazonDynamoDB connection() {
        return this.connection;
    }
}

It would look something like the code above.