That’s a lot of flood waters!
to deal with normal wetness, elevating the waterer would possibly help if the ducks are making it wet over there.
overall, you need to provide drainage. Many people suggest chipped wood, like from a tree guy. We did this, and put about 17-20 yards of chipped wood (his entire load) in our 50x10 run. It seemed like the chickens were eye level with us at first (they weren’t, of course). It settled down pretty quickly. We added random boards around the perimeter to keep the wood in. Water drains through…etc.
adding a roof. But, I don’t think that will really fix anything in your situation.
using pallets laid on the ground. Drawback: rodents may like the spaces underneath.
raising up one side with dirt, so it is sloped in a logical way to allow non-flood water to run off to a logical destination. LA is wet, so you would know best if this could work.
gravel- can work. My neighbor did this in his smaller run that was muddy. Lots of gravel to where normal rain did not have standing puddles or really wet mud. Neighbor did keep it well layered with straw/ mulch so they weren’t only on gravel.
pavers laid down in part of the run. Find free ones/broken ones, remodel throw seats -who cares if they match? Chickens don’t.
but, if you get floods, you may want to additionally consider elevated platforms made out of scrap or pallets (shade in non flood situations) so they can fly between the platforms and their roosts, move around if possible.
FWIW, we brought in 102 tons (4 truckloads) of dirt to level out the back and side of our property-low spots, minor flooding, water trapped. It has helped tremendously, and the ground was elevated only a couple inches, but low spots were filled in. We redirected the down spouts of the barn (next to chicken run) to actually flow away, and through longer pipes. We finally (after 3 years) have a roof over the run. But, our run backs up to the barn, so it is protected on one side.