Nicholson used seal skin in a cavity where the right thumb presses outwards in the three-point 19th century grip. At the base of the left index finger, he had a depression cut, effectively making the flute thinner here, not thicker. He recommended using the tips of L1 and L2, but the flat of L3. You see a lot of old flutes with fingernail grooves on L1 and L2.
Here’s the relevant stuff from Nicholson:
"The position of the flute should be nearly horizontal, being supported by placing the second joint (about an inch above the first hole) against the side of the first finger of the left hand, resting it nearly as high as the knuckles. By this means, that finger will have free action, and the second and third fingers can be more easily brought over the holes, than if the flute were placed lower down on the joint of the finger.
The first and second holes should be covered with the points of the first and second fingers; and the third hole by the third finger, using the broad part immediately under the nail. By which the first and second fingers become properly curved, the little finger will find its place exactly over the G# or Ab key, and the thumb will be over the A# or Bb key.
The thumb of right hand must press against the third joint of the flute, being placed nearly under the fourth and fifth holes, but nearer the fourth. The fingers must be curved, particularly the second. Great care must be taken to avoid the third being straight, for to this fault may be attributed the difficulty experienced by many amateurs in the use of the F natural and lower C keys. The little finger should be over the D# or Eb key.
This being understood, place the mouth-hole of the flute at the centre of the under lip, resting the instrument between that and the chin. With the pressure of the thumb of the right hand acting against the pressure of the first finger of the left, and the flute being placed to the lip, as here described, the instrument will obtain the proper and only support it should depend upon. This will be fully experienced when the pupil is sufficiently advanced to play in the keys of B with five sharps, or A with four flats. (Snip)
As this position of the instrument will be found somewhat difficult, it may in a great measure be relieved by pressing the thumb of the left hand on the second joint of the flute, just above the Bb key. So convinced am I, from long experience, of the necessity of the instrument being held with great firmness, that in order to accomplish it, I have a groove cut out of the second joint (about half the thickness of the wood) to receive that part or the finger on which the pressure lies, which brings the hand closer, and at the same time gives additional support to the instrument.
The third joint I have also grooved out on the part where the thumb presses and inserted a piece of seal-skin; which prevents the thumb from slipping and gives great firmness to the right hand." (Snip)
Terry