FLUTTER => Using Widget Sizes to calculate the Sizes of other widgets Automatically Or Manually

main.dart

import 'package:flutter/material.dart';
import 'dart:async';

//Desired Behavior on FIRST build (It should not take 3)
//CASE 1 (parent uses child size) : eye.width = vane.width * 10
//CASE 2 (child uses parent size) : pupil.width = iris.width / 2
//CASE 3: (child uses sibling size) : iris.width = vane.width * 5

//Desired Sizes (can be read from Render Tree in Flutter Inspector) [in original config of 4 letters]
//vane = 30
//pupil = 75
//iris = 150
//eye = 300

//NOTE: that vane width (aka size) is not determined until we see what is inside of it

void main() => runApp(new MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new StateFull();
  }
}

class StateFull extends StatefulWidget {
  @override
  _StateFullState createState() => new _StateFullState();
}

var vaneKey = new GlobalKey();
var vaneWidth;
var irisKey = new GlobalKey();
var irisWidth;

class _StateFullState extends State<StateFull> {

  //NOTE: change this to either run the rebuild in one shot or slowly see the progression
  bool automaticReBuilding = false;
  //NOTE: this starts here because the first build method isn't technically a rebuild
  int timesReBuilt = -1;
  //NOTE: this is set MANUALLY given the dependencies between your widgets
  //In this particular case C relies on B which relies on A
  //so (first) I get the size of A, (second) I use the size of A to get B, (third) i use the size of B to get C
  //which comes down to 3 rebuilds
  int requiredBuildsPerChange = 3;
  int timesBuilt = 0;

  rebuild(){
    setState(() {

    });
  }

  rebuildAsync() async{
    await Future.delayed(Duration.zero);
    setState(() {

    });
  }

  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {

    timesReBuilt++;

    if(automaticReBuilding){
      timesBuilt++;
      print("build #" + timesBuilt.toString());
      if(timesBuilt < requiredBuildsPerChange)
        rebuildAsync();
      else
        timesBuilt = 0;
    }

    var complexWidget = complexRelationshipWidget();

    return new MaterialApp(
      title: '3 Cases Test',
      home: new Scaffold(
        backgroundColor: Colors.brown,
        body: new Stack(
          children: <Widget>[
            new Align(
              alignment: Alignment.center,
              child: complexWidget,
            ),
            new Container(
              padding: EdgeInsets.all(16.0),
              alignment: Alignment.bottomRight,
              child: new RaisedButton(
                onPressed: () => (automaticReBuilding == false) ? rebuild() : null,
                child: new Column(
                  mainAxisSize: MainAxisSize.min,
                  children: <Widget>[
                    Icon(Icons.update),
                    new Text("Manual ReBuilds\nOR\nAutomatic Frame Stutter\n$timesReBuilt", textAlign: TextAlign.center,),
                  ],
                ),
              ),
            ),
          ],
        )
      ),
    );
  }

  Container complexRelationshipWidget() {

    vaneWidth = vaneKey?.currentContext?.findRenderObject()?.semanticBounds?.size?.width;
    irisWidth = irisKey?.currentContext?.findRenderObject()?.semanticBounds?.size?.width;

    return new Container( //-----EYE-----
        decoration: BoxDecoration(shape: BoxShape.circle, color: Colors.white),
        width: vaneWidth == null ? null : vaneWidth * 10,
        alignment: Alignment.center,
        child: new Row(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            new Container( //-----VANE-----
              key: vaneKey,
              color: Colors.red,
              child: new Text("vane"),
            ),
            new Container( //-----IRIS-----
              key: irisKey,
              decoration: BoxDecoration(shape: BoxShape.circle, color: Colors.blue),
              width: vaneWidth == null ? null : vaneWidth * 5,
              alignment: Alignment.center,
              child: new Container( //-----PUPIL
                decoration: BoxDecoration(shape: BoxShape.circle, color: Colors.black),
                width: irisWidth == null ? null : irisWidth / 2,
              ),
            ),
          ],
        )
    );
  }
}

Working Example (manual setting)