Test Data
DECLARE @TABLE TABLE(Customer_ID INT,App_ID INT,App_Date DATE)
INSERT INTO @TABLE VALUES
(200,13,'12/28/2013'),(200,23,'12/26/2013'),(300,11,'12/15/2013')
,(200,54,'12/15/2013'),(300,32,'12/15/2013'),(200, 9,'12/2/2013')
,(100, 6, '12/22/2013')
Query
; WITH CTE
AS (
SELECT *
,ROW_NUMBER() OVER (PARTITION BY Customer_ID ORDER BY App_Date) rn
FROM @table
)
SELECT C1.Customer_ID
,C1.App_ID
,C1.App_Date
,CASE WHEN DATEDIFF(DAY, C1.App_Date, C2.App_Date) <= 7
THEN 1 ELSE NULL END AS Flag
FROM CTE C1 LEFT JOIN CTE C2
ON C1.rn = C2.rn + 1
AND C1.Customer_ID = C2.Customer_ID
Result Set
╔═════════════╦════════╦════════════╦══════╗
║ Customer_ID ║ App_ID ║ App_Date ║ Flag ║
╠═════════════╬════════╬════════════╬══════╣
║ 100 ║ 6 ║ 2013-12-22 ║ NULL ║
║ 200 ║ 9 ║ 2013-12-02 ║ NULL ║
║ 200 ║ 54 ║ 2013-12-15 ║ 1 ║
║ 200 ║ 23 ║ 2013-12-26 ║ 1 ║
║ 200 ║ 13 ║ 2013-12-28 ║ 1 ║
║ 300 ║ 11 ║ 2013-12-15 ║ NULL ║
║ 300 ║ 32 ║ 2013-12-15 ║ 1 ║
╚═════════════╩════════╩════════════╩══════╝