I read somewhere that chemical fertilizers, like the blue stuff we see...
We assume you are speaking of products such as Miracle Gro or Miracid. These are diluted in water and poured or sprayed on plants.
These fertilizers are what's known as "quick release", meaning the particles dissolve immediately in the water and are in a form available for rapid uptake by plant roots. Yes, if there was a heavy rain that occurred immediately after the fertilizer was applied, it's possible the rain would wash a lot of the nutrients farther down into the soil below where the plant's roots are. (Although even a granular fertilizer applied to the soil surface gets washed away in a deluge.)
This type of fertilizer is excellent for a first application when planting young vegetable transplants or other plants such as perennials, shrubs and trees. The nutrients are instantly available as the plant is getting established in its new location.
However, this fertilizer is not going to last long. In the case of vegetables, many vegetables need to be fertilized again during the growing season and usually not with a quick release fertilizer like Miracle-Gro. Instead a standard granular garden fertilizer is used. It's still available pretty fast. For long term fertilization, use an organic fertilizer that decomposes or breaks down slowly, such as compost. This is better and more natural for shrubs and trees, Established shrubs and trees do not need to be fertilized at all, especially not with synthetic fertilizers.