What I think you’re talking about is cranning.
The old-school whistlers, at least the guys I heard back in the 70s when I was learning, didn’t do crans on Bottom D or Middle D either one. (In Irish music it’s usual practice to speak of notes as if a D instrument is being played, regardless of what pitch instrument is actually being played at the moment. This is done on uilleann pipes, flute, and whistle.)
I would have to hear the tune in question, or the passage in question, but the old-timers would find another way to express it, rather than doing a triplet on the same note the way a fiddler or tenor banjo would do. Ditto for the box, they would find another way to express it, rather than hammer out three D’s in a row.
Traditionally uilleann pipers would cran Bottom D and sometime Low E, but for Middle D (called Back D on the pipes due to the thumbhole) they would, like whistle and flute and box players, find a melodic solution for passages in which a fiddle or tenor banjo was played a triplet of repeated Middle D’s. What they would do (and mostly still do) depends on the context, the shape of the melody at that point, and what the function of the triplet is.
Then, on the pipes, probably in the 1960s or around early 1970s, Finbar Furey made famous a stuttering triplet on Back D done by rapidly swiping the thumb back and forth over the hole. Paddy Keenan began doing it, as far as I can tell, around the same time. I believe that Donald MacLeod, the famous Highland piper and composer and arranger, was doing it earlier, by the 1950s at least, and composed at least one tune with these thumb triplets incorporated into it. This technique has since become, on both Highland and uilleann pipes, SOP more or less.
The bottom line is that there is no need for crans to be done on the whistle or flute. They’re a technique borrowed from the pipes fairly recently (credit usually given to Matt Molloy).
The advantage is that on the whistle and flute the exact pipers’ cran for Bottom D works equally well on Middle D (unlike on the pipes).
With cranning, the “rules” (traditional norms) say that the fingers used for the cuts are the tophand ring finger, and the index and middle fingers of the bottom hand. Just what sequence these cuts are in varies from piper to piper, but the “rule” is that no one finger should be used twice in a row. Some traditional sequences are
F# G A
G F# A (Willie Clancy’s)
A F# G
and any other.
Then there’s a longer cran with four cuts such as
G F# G A
and so forth.
When executed correctly these have a wonderful bubbling sound.
On whistle you can play Middle D either closed or open depending on your whim or how you prefer it to sound.
I’m not a fan of triple-tonguing on the whistle or Irish flute. If I’m going to borrow points of technique from another instrument I’d rather it be a traditional Irish instrument like the pipes rather than an orchestral or jazz instrument like the Boehm flute.