You are talking about doing a search type application where only existing values are shown.
To do this you would need to do a query to get all of the posts, loop over them and see what is set. This would be a time consuming process.
The other option is to keep track of what is available.
But there isn’t any way to find out which values are selected directly.
Unless you’re saying that the checkbox field is a taxonomy field and then that would be a completely different story. But if this is the case it is not obvious from your description.
