First, thank
f95toli and M Quack for providing the information.
The specific references are:
R. Doll and M. Nabauer, Phys. Rev. Lett. 7, 51 (1961); and
B. S. Deaver and W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).
(In fact, in some articles they are cited in a "3 in 1" manner together with: N. Byers and C. N. Yang, Phys. Rev. Lett. 7, 46 (1961)).
Of the NIST listing relating to flux quantum, the paper "
Absolute determination of the magnetic flux quantum using superconducting magnetic levitation" looks promising, but I do not have access to the full text now. I will try later. But I doubt if they directly measured flux quantum, as Doll and Nabauer did. Specifically, if they simply measured the the Josephson constant and toke inverse of the latter as their flux quantum, it could be meaningless to physics topics like "is the flux quantum a fraction/multiple of hc/e?"