The reasons why some words flourish and others fall by the lexical wayside are often unclear, but what is clear is that slimsy is firmly in the latter category: it has very little current use. This doesn't have to stop you from using it though; slimsy is a blend of slim and flimsy, and its meaning should be pretty much apparent to your audience if you're careful with the context. The word was first used in the mid-19th century and was at its peak of popularity in the early 20th, but who knows? Maybe the 21st century will see its revival.
