Examples of how to change the capabilities for what kind of user can use Caldera Forms admin via the caldera_forms_manage_cap filter SEE: https://calderaforms.com/doc/caldera_forms_manage_cap/

caldera_forms_manage_cap1.php

<?php
/**
Allow users with the editor role to use the Caldera Forms admin screen
*/
add_filter( 'caldera_forms_manage_cap', function( $cap, $context ) {
	if( 'admin' == $context ) {
		return 'edit_pages';
	}

	return $cap;
}, 10, 2 );

caldera_forms_manage_cap2.php

<?php
add_filter( 'caldera_forms_manage_cap', function() {
	return 'delete_posts';
}, 51 );

caldera_forms_manage_cap3.php

<?php
/**
Change capability for editting Caldera Forms entires
*/
add_filter( 'caldera_forms_manage_cap', function( $cap, $context ) {
	if( 'edit-entry' == $context ) {
       //choose a capability of the role you wish to allow
		return 'create_posts';
	}

	return $cap;
}, 10, 2 );

/**
Change capability for deleting Caldera Forms entires
*/
add_filter( 'caldera_forms_manage_cap', function( $cap, $context ) {
	if( 'edit-entry' == $context ) {
		//choose a capability of the role you wish to allow
		return 'edit_pages';
	}

	return $cap;
}, 10, 2 );

Any luck with this? I haven't been able to resolve this issue.