I think this is considerably harder to be categorical about, but let me float a theory and see if it seems to make sense.
But first, we need to note that in these flat footed flutes, it’s not just the D that is flat. Low Eb is usually worse, and low C# worse again. Normally the C isn’t bad. So we have to look for a reason for that pattern.
By the mid 18th century, they were getting pretty good at making flutes. Four keys were common, with the flute ending at D. Makers at the time had found that if they continued the taper to the bottom the low D was distinctly flat. My modelling suggests that this is because if you taper the bore enough to get all the other notes in tune with their octaves, the cumulative effect will be too great by the time you get to the bottom. Fortunately, they also determined that if they flared the bottom of the bore, by the simple expedient of reversing the same reamer and coming in from the bottom, they could fix that.
But then some bright spark got the idea that the flute should go down to C. That required them to do away with the flare, and extend the taper down past where D was now a side hole, past C#, before a small flare could be introduced. That small flare was enough to get C back in tune, but low D, Eb and C# were terribly flat.
I suspect it wasn’t helped when Nicholson “improved” the flute by enlarging particularly holes 2 and 5. That would make the body notes sharper. Nobody mentioned shortening the foot to bring those notes up too.
I suspect another contributing confusion was that of pitch. At the start of the century, the pitch was circa 410. We commemorate that with modern “baroque pitch” at 415Hz. But it was on the way up, and soon settled at 430Hz, before the young bucks in the Philharmonic movement pushed it up to 455. So flutes should have been shortening, without which the foot notes were going to tend flat anyway. They were getting shorter, but not at the rate the pitches would seem to demand. Complicated by the fact that the same flute had to do for both pitches!
So I think we probably had a number of things going on, all contributing to flat feet. From about Nicholson on, things started to get better. I have yet to confirm how this happened, and at whose hands, and by what methods, but I think we can assume that it related to increasing the bore in the lower RH and foot area. Essentially, the taper had been overdone, which probably became more and more obvious as pitch rose.
I think Boehm’s 1832 conical would have come as a kick in the bum to other flute makers, and we certainly see Siccama sorting stuff out around 1847. Then of course Boehm returns with the very well tuned cylindrical bore - another kick in the bum! Pratten responds with his Perfected (really a Siccama restored to 8 keys) and the problem is just about fixed. Significantly, Siccama and Pratten have reduced the length and the taper angle so that the foot bore is not so small.
Interestingly, Rudalls pretty much carried on with the old model, but then the majority of their work was in selling cylinder flutes, so they can probably be excused. They did snap to around 1895 when high pitch was abandoned in favour of something close to modern pitch. But that meant that they had missed the whole high pitch thing! But only in their conical flutes - their cylinder flutes were definitely aimed at high pitch.
Irish players in the 60’s onwards worked out ways to play to get around this flatness, and it’s probable that similar approaches were used back in the period. Carte and Ward (both on my web site) both comment on tuning as a real problem. Eg Ward:
Akin to this mystification, is the course pursued in many instruction books. We have not seen one which candidly informs the learner of the manoeuvres required to play the ordinary flute in tune. They give a vast variety of modes of fingering the same notes; with the object, one might suppose, of perplexing the scholar, or of showing the author’s ingenuity. Their silence on the one hand, and their profuse loquacity on the other, furnish strong evidence of their having (in the old flute) a bad case to deal with, requiring a large amount of special pleading, and a studious concealment of the important truths.
The authors of these books do not tell the student that the intonation of the instrument rests entirely with the performer, and depends upon certain zig-zag manoeuvrings of his lip, and other subterfuges. They do not point out which notes require the flattening or sharpening, the forcing or tempering process. Oh, no! the flutes they recommend are, doubtless, well in tune: the student is to blame if he cannot play in tune; and he must take expensive lessons to learn, not how to tutor his own ear, but to correct the false intonation of the instrument.
Ah, lovely stuff!
Terry