You can use the following shortcode to display the custom field on the front end post:
[bp-member-blog-custom-field key="oembed-field"]
The key attribute should be set to the unique meta key that was assigned when creating the custom field. This key identifies the specific custom field you want to display on the front end. For example, if the unique meta key for your custom field is “oembed-field,” you would use that in the shortcode.

The site admin can edit the blog and insert the shortcode to display the custom field on the frontend.

