Permissions to access an object are generally a matter of both a user's profile and any permission sets that have been assigned to them. In this particular case, since you're talking about a list view, you're going to want to first take into consideration access to records of the parent object since the list view would be considered a child of that object. Without access to records that are included in that list view, a user won't have access to it.
I believe the data that you're looking for is hidden in the SetupEntityAccess. You'll see a visual model of the ERD here.
I think your query should look something like:
SetupEntityAccess accessSettings = [SELECT Id FROM SetupEntityAccess WHERE
SetupEntityId IN (SELECT Id FROM ListView WHERE NamespacePrefix = :your_namespace
AND Name = :Your_List_View) AND ParentId IN (SELECT PermissionSetId
FROM PermissionSetAssignment WHERE AssigneeId = :UserInfo.getUserId()) LIMIT 1];
Note: that you may need to run a separate query restructured around ObjectPermissions depending on how you're granting access to the records.
You may want to see @eyescream answer to this related post: How do I find out if a user has access to a visualforce page through apex?.
I did some further research, including using Workbench to check the metadata on
SetupEntityAccess. I discovered that
SetupEntityAccess is not the object to be running your query on, and that
ListView is not one of its children. Going beyond that, I don't even think that
ListView is what you want to be looking at as your starting point!
Instead, I believe the object that you're looking for is
UserListView! One of its children is
UserListViewCriterion. Some of its fields include
sObjectType (all standard objects + custom objects),
UserId. I believe this is what you're looking for and that you can run a direct query on it since it is queryable.
UserListView is a child of
ListView, so you should be able to relate
UserListView back to the
ListView for each object that you're interested in. While there is no
CustomObject to query on, that's what the metadata API showed the
ListView being a child of. That suggests to me that each
ListView is a child of each
sObjectType that it's created for. I've not constructed a query, but I'd suggest an approach that either uses
UserListView in a subquery for
ListView or vice-versa since the two are closely related while at least specifying the
sObject and perhaps a list of UserIds to select from.
I hope this points you in the right direction to find the results that you're looking for.