If I understand your question correctly, you have multiple items and you want them to be independently checkable.
To do that you will need for them to each have their own state value. How you do this will depend on your design needs, but form your code you would need to have an array instead of the check1 state.
Something like this:
this.state.allItems.map((res, index) => {
return(
<CheckBox
color="green"
style={{ marginRight: 20, }}
checked={this.state.checked[index]}
onChange={()=> {
let { checked } = this.state;
checked[index] = !checked[index];
this.setState({checked});
}
}
/>
Of course you will need to populate the checked state properly with an array.