End date day count

You could create a calculated column like

Day count =
VAR EndDate = 'Table'[End Date]
VAR NextStartDate =
    CALCULATE (
        MIN ( 'Table'[Start Date] ),
        ALLEXCEPT ( 'Table', 'Table'[Location], 'Table'[Kennel] ),
        'Table'[Start Date] >= EndDate
    )
VAR Result =
    DATEDIFF ( EndDate, COALESCE ( NextStartDate, TODAY () ), DAY )
RETURN
    Result

RichOB Create a calculated column to find the next start date for each kennel:

Next Start Date =
VAR CurrentKennel = 'Table'[Kennel]
VAR CurrentEndDate = 'Table'[End Date]
RETURN
CALCULATE(
MIN('Table'[Start Date]),
FILTER(
'Table',
'Table'[Kennel] = CurrentKennel &&
'Table'[Start Date] > CurrentEndDate
)
)

Create a calculated column to calculate the day count:

DAX
Day Count =
VAR NextStart = 'Table'[Next Start Date]
VAR CurrentEnd = 'Table'[End Date]
RETURN
IF(
ISBLANK(NextStart),
DATEDIFF(CurrentEnd, TODAY(), DAY),
DATEDIFF(CurrentEnd, NextStart, DAY)
)