I don’t have any literature or specs for you but, if flooding compaction is the same as what we call hydro-compaction, I should tell you that hydro-compaction is expressly forbidden here in Ventura County California..

I don't know that there's any documentation on the subject, either.  My understanding is that it's somewhat like when you go to the beach.  Sand further away from shore is loose, whereas when you get right up to it, the sand is very hard.  I would say that this would only work for a well-graded sand with little or no material passing the #200.  As you probably know, silt has a habit of hanging on to water, and what you would end up with is mud.  

Best of luck with your contractor.  Just a though; he may be used to that method, but I'm sure he's used a jumping jack before.  

Works really good to pre-settle, especially around manhole and simialr objects. Simulates a rising and then falling water table, so when that eventually happens it will have far less effect. The flooding tends to even out the filled area more uniforly and lessen any voids and such that may have formed during backfill but prior to paving.

I only know of this being done by contractors on their own after compaction of utility trench prior to paving. I dont know of any real specifications, and this is supplemental to the compaction criteria.

Take some moist soil, dump it around a manhole or in a utility trench across a road.  The dry density of the soil will be well below the minimum dry density of that soil.  Add water, and the soil will be slightly above the minimum dry density of the soil.

When the road settles over time in those areas, the municipality will have you on the phone-not the contractor.

I'm not a fan of "puddling" sandy fill.  I have had to put up with a lot of contractors saying how great it is.  In the few instances where they used it (permitted by the "authority"), we ended up with settlement problems.  How does the water "compact" the sand - it is by seepage pressure.  Unless you have a large seepage head, I cannot be convinced that the compaction will be what you want.  In trenches, where is the potential water head?  Not much.  If water can compact, then why do we run into many sandy deposits with N values in the order of 3 to 5?  Now, having said this, I did use it once - to compact a river sand backfill behind a retwall - a chimney void of about 1 m between free standing diamicton (till-like) soil and the retwall.  But, I had more than 15 m of head - so when we washed the sand down, we had quite a bit of pressure.  As MRM says, be wary.