How to style FormControlLabel font size

You could define the label as a Typography component and apply the style there:

<FormControlLabel 
    control={<Checkbox value="Hello" color="primary" />}
    label={<Typography style={styles.formControlLabel}>World</Typography>}
/>

UPDATE:

As per Saber’s comment, newer versions should instead use:

<FormControlLabel 
    control={<Checkbox value="Hello" color="primary" />}
    label={<Typography className={styles.formControlLabel}>World</Typography>}
/>