The Puget Sound region is wedged between the Pacific and the Cascades...you'd think with all that rain (and snowmelt in the warmer months), there would be catastrophic flash flooding in lowland areas, of the magnitude seen in Oklahoma (1, 2, 3), Texas (1, 2, 3, 4) or Tennessee (1, 2, 3).
Regarding climate, it does not rain in Seattle as much as people think; Seattle is in the snow shadow of the Olympic Mountains. It doesn't rain much in summer at all. Seattle gets rather dry in July and August.
Regarding flooding, the Skagit and Snohomish rivers north of Seattle flood regularly experience flooding. Some of the land in the flood plain is used for farming, and there are scattered households in the 100 year flood plain.
Regarding drought, drought severity is relative to the amount of precipitation and soil moisture levels typical for a specific locale. This means that even a rainforest can suffer drought. Because it's a relative concept, the rainfall during a drought in a rainforest would be a rainfall bonanza in arid climates.
Regarding forest fires, the Seattle area occasionally undergoes offshore flow. This occurs when the air pressure is lower in the Seattle area than it is east of the Cascades. This makes winds blow from the east, and if there's a forest fire east of the Cascades (which has a rather dry climate), that smoke can be carried westward toward the Seattle area by the offshore flow. That said, wildfires have occurred on the western slopes of the Cascades, and sometimes even in the temperate rainforest to the west of the Seattle area.
Catastrophic flash flooding is usually a sign of poor city/road planning in flat areas or due to torrential downfall of rain. The reality is that all the terrain in Washington allows water to drain, rather than be left standing (which causes flash flooding). And let's be clear, it doesn't rain hard in WA, it's usually not torrential downpour, bur rather a slow methodical drizzle that can easily drain away down rivers and streams. A lot of development in the mid-west ignores known flood plains.
As for your comment about wildfires, WA gets it's rain in the cold seasons. So there is usually very dry weather in the summer when wildfires occur.
We do get flooding in the Puget Sound lowlands, but it actually happens most often when a mid-winter warm front brings a moderate amount of rain to higher elevations, causing sudden, extensive snowmelt.
Those weather systems, like one in February 2020 that caused quite a bit of flooding, suddenly raise temps by 15-20 degrees C (20-30 °F), and raise the snow/rain threshold up by 1000 meters (a few thousand feet) or more overnight. Even though the rainfall totals in those storms are usually not that great by comparison with the major storms in the South or the Plains, 5 cm/day (1-2 inches per day), the net effect is that a huge amount of water enters waterways all at once.
Even so, the steep slopes in the area generally mean that flooding is limited to a few river valleys. Our elevation profile goes from 3000 meters (8000 feet) to sea level in about 50 km (30 miles), so that water heads downhill FAST.
Because soil drainage would be higher and the ground would take long to saturate Floods don't always happen in Rainy weather all the time because first the soil needs to be saturated (the point where it filled up with water) then the rain needs to continue, Flash floods are mostly produced this way.
So you would need lots of rain for a flood to occur in WA, I mean lots.
To add some concrete data to some of the great answers already here:
Seattle is actually not particularly rainy, especially compared to other parts of WA, but also compared to other cities in the US. According to this chart of the largest 51 US cities, Seattle is wetter than 18, drier than 31, and tied with 1. Yet, Seattle only has less rainy-days than 5 cities, and more rainy-days than 45 cities. This indicates that Seattle probably gets its rain as a constant drizzle (which seems confirmed from anecdotal evidence) which would allow for the area to store and drain water faster than it peaks.
A unexpected city that does suffer from flash floods is Tuscon, Arizona. It receives 11.6 inches (294.6 mm) of rain yearly and 2.4 inches (61 mm) in its peak month. It is, however, flat and apparently large parts of the city do not have storm sewers. Additionally, the Arizona habitat does not seem to naturally drain water very well. This shows the importance both of city planning and natural drainage, which I'm sure Seattle, a wet city, has both in plenty.