I did a little more testing, and came up with a simple solution using a trigger:

CREATE TRIGGER [dbo].[BitTrigger]

ON [dbo].[Table2]

FOR INSERT, UPDATE

AS BEGIN

DECLARE @Result BIT

DECLARE @Flags INT

SELECT @Flags = Flags FROM inserted

SELECT @Result = CASE WHEN SUM([Value]) & @Flags = @Flags THEN 1 ELSE 0 END

FROM Table1

IF @Result = 0 BEGIN

RAISERROR ('This is not an acceptable combination of values.', 16, 1)

ROLLBACK TRANSACTION

END

END