"As Gabrielle was impacting the east coast of Mexico, Hurricane Flossie in the Eastern Pacific was battering the Baja Peninsula" - the "as" is ambiguous. Does it mean "because"? "as a result of"? "Since"? It's not an ideal sentence starter. Also, could you use a less dramatic word than "battering"? It just makes me hungry and think of waffles.
"totaling to at least 19.44 inches (494 mm). " - why the "at least"? HPC says that was the peak. I think you should also say "peaking" instead of "totaling to". You should mention the HPC peak in the impact section too.
"From the outset, its motion was hampered by that of Hurricane Flossie off the Pacific coast of Mexico" - poor start to a paragraph. You should say "the cyclone's" or something instead of "its". Also, was the motion really "hampered"? That sounds like a negative thing.
"at first. Deep convection fired up only gradually at first" - cut one of the "at first". Also, in that sentence, it doesn't seem like it took that long to strengthen. 18 hours as a TD isn't unusual.
"The track also shifted southward somewhat, shifting the threat from Texas into Mexico" - was the storm ever supposed to strike Texas? Also, remove one of the "shift"
Including the final sentence in the previous paragraph, you have consecutive sentences starting with "The storm". Liven it up a bit!
"Rains from Gabrielle flooded streets and destroyed bridges and highways in northern Mexico, which is an industrial capita" - a large region of Mexico is an industrial capital?