If you have that many items, it's probably best to initialize them using Java, rather than using FXML. For example, instead of:
<FlowPane fx:id="container" minWidth="..." minHeight="...">
    <Label fx:id="label1" text="Label 1"/>
    <Label fx:id="label2" text="Label 2"/>
    <Label fx:id="label3" text="Label 3"/>
    <!-- ... -->
    <Label fx:id="label1000" text="Label 1000"/>
</FlowPane>
and a controller 
public class Controller {
    @FXML
    private FlowPane container ;
    @FXML
    private Label label1 ;
    @FXML
    private Label label2 ;
    // ...
    @FXML
    private Label label1000 ;
    // ...
}
I would do
<FlowPane fx:id="container" minWidth="..." minHeight="...">
</FlowPane>
and
public class Controller {
    @FXML
    private FlowPane container ;
    private List<Label> labels ;
    public void initialize() {
        labels = new ArrayList<>();
        for (int i = 1; i <= 1000; i++) {
            Label label = new Label("Label "+i);
            labels.add(label);
            container.getChildren().add(label);
        }
    }
}
As a variation on this idea, consider defining a custom component:
public class LabelFlow extends FlowPane {
    private List<Label> labels ;
    public LabelFlow(@NamedArg("numLabels") int numLabels) {
        labels = new ArrayList<>();
        for(int i = 1 ; i <= numLabels ; i++) {
            Label label = new Label("Label "+i);
            labels.add(label);
        }
        getChildren().addAll(labels);
    }
    public List<Label> getLabels() {
        return Collections.unmodifiableList(labels);
    }
}
Now in your FXML you do 
<LabelFlow fx:id="labelFlow" numLabels="1000"/>
and in your controller
public class Controller {
    @FXML
    private LabelFlow labelFlow ;
    public void initialize() {
        for (Label label : labelFlow.getLabels()) {
            // do whatever you need with label....
        }
    }
}
You need to jump through a couple of hoops if you want to use a custom class like that in Scene Builder. See Adding a custom component to SceneBuilder 2.0
If you really want to define all those controls in FXML, which would be a maintenance nightmare imo, you can use reflection to access the variables. I don't recommend this, not just because it's hard to maintain, but also because reflection by its nature is error-prone (no compile-time checking) and complex.
But you could do
public class Controller {
    @FXML
    private FlowPane container ;
    @FXML
    private Label label1 ;
    @FXML
    private Label label2 ;
    // ...
    @FXML
    private Label label1000 ;
    private List<Label> labels ;
    public void initialize() throws Exception {
        labels = new ArrayList<>();
        for (int i = 1; i <= 1000; i++) {
            Field field = getClass().getDeclaredField("label"+i);
            boolean wasAccessible = field.isAccessible();
            field.setAccessible(true);
            Label label = (Label) field.get(this);
            field.setAccessible(wasAccessible);
            labels.add(label);
        }
    }
}