You will have to run a query to get the data. You should be able to run the following against the member_group field of the member.
SELECT exp_channels.channel_title, exp_channel_fields.field_label, exp_channel_fields.field_name, exp_channel_fields.field_type, exp_channel_member_groups.channel_id FROM exp_channels, exp_channel_fields, exp_channel_member_groups WHERE exp_channel_member_groups.group_id = '6' AND exp_channel_member_groups.channel_id = exp_channels.channel_id AND exp_channels.field_group = exp_channel_fields.group_id
So in EE, run a exp:query like this maybe: (Should at least get you going)
Member Group : {member_group}<br>
<table>
<thead>
<tr>
<th>Channel</th>
<th>Field</th>
<th>Type</th>
<tr>
</thead>
<tbody>
{exp:query sql="
SELECT channel_title, field_label, field_name, field_type
FROM exp_channels a
JOIN exp_channel_member_groups b on b.channel_id = a.channel_id
JOIN exp_channel_fields c on c.group_id = a.field_group
WHERE b.group_id = '7'
"}
<tr>
<td>{channel_title}</td>
<td>{field_label} - {field_name}</td>
<td>{field_type}</td>
</tr>
{/exp:query}
</tbody>
</table>
Of course, you'll have to figure a way to get your member's {group_id} into where '7' is now.