On my 1850 flute Firth & Pond, I did not find the C & C# easy to play at first, although they are now coming along. For that matter, the D note was slightly harder to seal when compared with other flutes, perhaps due to the hole’s size or its location being a little lower down; not sure why.
(1) Breath control is harder the lower you go.
(2) If the right ring finger moves ever so slightly, you lose the C notes. Sealing the D hole takes some practice. I notice in Jem’s video that his right ring finger moves a little when he reaches for the C, despite which he successfully plays the C notes.
(3) Maybe the Eb key doesn’t seal properly - pad or spring issue. Try a rubber band on that key to verify.