I must change your question to this:

 

That's because the way you have it stated,

the answer would depend on the flush that you are talking about, for a higher
flush beats a lower flush. For instance, a queen-high flush beats a jack-high
flush or any other flush with a lower high card.  


First we'll find the number of possible hands that are 

(1) flushes (straight or not), 
(2) full houses, 
or 
(3) 4-of-a-kind's 

Then we'll subtract from the total number of poker hands with 5 cards, which is
C(52,5). Then we'll divide by C(52,5).

Flushes and straight flushes
The total number of flushes and straight flushes is C(4,1)×C(13,5) because for
each of the C(4,1) ways to choose the 1 suit, there are C(13,5) ways to choose
the 5 denominations. That's C(4,1)×C(13,5) = 5148

The number of full houses is C(13,1)C(4,3)C(12,1)C(4,2) because for each of the
choices of denomination for the three that are alike, we choose 3 suits for
them. Then for each of the choices of the 12 remaining denomination for the two
that are alike, we choose 2 suits from them.
C(13,1)C(4,3)C(12,1)C(4,2) = 3744

The number of 4-of a kind's is C(13,1)×C(48,1) because for each of the ways you
can choose the denomination of the 4, there are 48 ways to choose the 5th card.
That's C(13,1)×C(48,1) = 624

Therefore the total number of flushes (straight or not), full houses, and
 4-of-a-kind's are 5148 + 3744 + 624 = 9516

The total number of 5-card hands are 2598960, so the number of hands that will
lose to the lowest possible flush are  2598960-9516 = 2589444

So the chances of being dealt a hand that will lose to the lowest possible
flush is  which reduces to  = .9963385354.

Round that however you are told.

Edwin