Major, gage-wrecking peaks are measured post facto by variants on the technique used by the early gage readers. Because the real peaks carry the remains of the gage away to California, the highwater marks are surveyed, resulting in a slope and bed perimeter measurement. From this and known roughness constants, the discharge can be calculated. Other techniques are also used, depending on the site.
Browsing the peak values, the failure of Teton Dam apparently "wins" for the continental United States: 2.3 million cfs. We are waiting for the data from the failure of Auburn Coffer Dam in 1986, and we have heard rumors of a reversing flood in Florida where a spring tide and a hurricane shoved a hump of about 4 million cfs upriver, setting a reverse record and then a drainage record the next day. Missing from the database is our favorite, the Spokane Flood, which apparently crested at about 9.5 cubic miles/hr (400 million cfs) according to J Harlan Bretz; by the time (some 20,000 years after that Pleistocene event) reliable estimating techniques were invented, the highwater marks were obscured, so precision is not possible. We know of no estimates for the Noachic deluge or the flood of Deucalion.