ConstraintLayout: square views, evenly distributed, autosized

You need to create a chain of widgets that is connected on all sides of its parent container (you set the dimensions of this parent container to whatever you want/need). Each widget should have the app:layout_constraintDimensionRatio="1:1" constraint to ensure a square pattern. For instance:

<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout 
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:orientation="horizontal"
android:layout_width="match_parent"
android:layout_height="match_parent">

<FrameLayout
    android:id="@+id/frame1"
    android:layout_width="0dp"
    android:layout_height="0dp"
    app:layout_constraintDimensionRatio="1:1"
    app:layout_constraintBottom_toBottomOf="parent"
    app:layout_constraintLeft_toLeftOf="parent"
    app:layout_constraintRight_toLeftOf="@+id/frame2"
    app:layout_constraintTop_toTopOf="parent"
    />

<FrameLayout
    android:id="@+id/frame2"
    android:layout_width="0dp"
    android:layout_height="0dp"
    app:layout_constraintDimensionRatio="1:1"
    app:layout_constraintBottom_toBottomOf="parent"
    app:layout_constraintLeft_toRightOf="@+id/frame1"
    app:layout_constraintRight_toLeftOf="@+id/frame3"
    app:layout_constraintTop_toTopOf="parent"
    />

<FrameLayout
    android:id="@+id/frame3"
    android:layout_width="0dp"
    android:layout_height="0dp"
    app:layout_constraintDimensionRatio="1:1"
    app:layout_constraintBottom_toBottomOf="parent"
    app:layout_constraintLeft_toRightOf="@+id/frame2"
    app:layout_constraintRight_toRightOf="parent"
    app:layout_constraintTop_toTopOf="parent"
    />

</android.support.constraint.ConstraintLayout>

Use Guidelines with precentage, something like this:

<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout 
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:orientation="vertical"
android:layout_width="match_parent"
android:layout_height="match_parent">

<android.support.constraint.Guideline
    android:layout_width="wrap_content"
    android:layout_height="0dp"
    android:id="@+id/guideline"
    app:layout_constraintGuide_begin="316dp"
    android:orientation="horizontal" />

<Button
    android:id="@+id/button2"
    android:layout_width="0dp"
    android:layout_height="wrap_content"
    android:layout_marginBottom="8dp"
    android:layout_marginLeft="8dp"
    android:layout_marginRight="8dp"
    android:layout_marginTop="8dp"
    android:text="Button"
    app:layout_constraintBottom_toTopOf="@+id/guideline"
    app:layout_constraintLeft_toLeftOf="parent"
    app:layout_constraintRight_toLeftOf="@+id/guideline2"
    app:layout_constraintTop_toTopOf="parent"
    app:layout_constraintHorizontal_bias="0.0"
    app:layout_constraintVertical_bias="0.502" />

<android.support.constraint.Guideline
    android:layout_width="wrap_content"
    android:layout_height="0dp"
    android:id="@+id/guideline2"
    android:orientation="vertical"
    app:layout_constraintGuide_percent="0.2" />

<Button
    android:id="@+id/button3"
    android:layout_width="0dp"
    android:layout_height="wrap_content"
    android:layout_marginBottom="8dp"
    android:layout_marginLeft="8dp"
    android:layout_marginRight="8dp"
    android:layout_marginTop="8dp"
    android:text="Button"
    app:layout_constraintBottom_toTopOf="@+id/guideline"
    app:layout_constraintLeft_toLeftOf="@+id/guideline2"
    app:layout_constraintRight_toLeftOf="@+id/guideline3"
    app:layout_constraintTop_toTopOf="parent"
    app:layout_constraintHorizontal_bias="0.0"
    app:layout_constraintVertical_bias="0.502" />

<android.support.constraint.Guideline
    android:layout_width="wrap_content"
    android:layout_height="0dp"
    android:id="@+id/guideline3"
    android:orientation="vertical"
    app:layout_constraintGuide_percent="0.4" />

<Button
    android:id="@+id/button4"
    android:layout_width="0dp"
    android:layout_height="wrap_content"
    android:layout_marginBottom="8dp"
    android:layout_marginLeft="8dp"
    android:layout_marginRight="8dp"
    android:layout_marginTop="8dp"
    android:text="Button"
    app:layout_constraintBottom_toTopOf="@+id/guideline"
    app:layout_constraintLeft_toLeftOf="@+id/guideline3"
    app:layout_constraintRight_toLeftOf="@+id/guideline4"
    app:layout_constraintTop_toTopOf="parent"
    app:layout_constraintHorizontal_bias="0.0"
    app:layout_constraintVertical_bias="0.502" />

<android.support.constraint.Guideline
    android:layout_width="wrap_content"
    android:layout_height="0dp"
    android:id="@+id/guideline4"
    android:orientation="vertical"
    app:layout_constraintGuide_percent="0.6" />

<Button
    android:id="@+id/button5"
    android:layout_width="0dp"
    android:layout_height="wrap_content"
    android:layout_marginBottom="8dp"
    android:layout_marginLeft="8dp"
    android:layout_marginRight="8dp"
    android:layout_marginTop="8dp"
    android:text="Button"
    app:layout_constraintBottom_toTopOf="@+id/guideline"
    app:layout_constraintLeft_toLeftOf="@+id/guideline4"
    app:layout_constraintRight_toLeftOf="@+id/guideline5"
    app:layout_constraintTop_toTopOf="parent"
    app:layout_constraintHorizontal_bias="0.5"
    app:layout_constraintVertical_bias="0.503" />

<android.support.constraint.Guideline
    android:layout_width="wrap_content"
    android:layout_height="0dp"
    android:id="@+id/guideline5"
    android:orientation="vertical"
    app:layout_constraintGuide_percent="0.8" />

<Button
    android:id="@+id/button6"
    android:layout_width="0dp"
    android:layout_height="wrap_content"
    android:layout_marginBottom="8dp"
    android:layout_marginLeft="8dp"
    android:layout_marginRight="8dp"
    android:layout_marginTop="8dp"
    android:text="Button"
    app:layout_constraintBottom_toTopOf="@+id/guideline"
    app:layout_constraintLeft_toLeftOf="@+id/guideline5"
    app:layout_constraintRight_toRightOf="parent"
    app:layout_constraintTop_toTopOf="parent" />
</android.support.constraint.ConstraintLayout>

To add Guideline, right-click on ConstraintLayout / Add Vertical/Horisontal Guideline... Hope it helps you

Cheers