Can someone learn how to write without natural talent? Is there a way to develop a unique writing style?

Everyone has to learn how to write, and writers just need to learn it better. I suppose the best thing is to practice, perhaps writing short stories, and to read books or short stories in a style you like and would like to imitate to some extent. I recommend imitation as a way to get started, then once you understand the fundamentals, begin experimenting with your style. Try out new ideas, be flamboyant, or overly serious, flirtatious. Just imagine what might seem interesting to you and give it a try.