It's a recurring problem with a lot of writers, and with myself in particular, when writing comes out feeling flat or unexplored. The writing has all of its structure there - A leads to B leads to C, all of the pieces are in place, but somehow, for some reason, it just doesn't pop. Something is not there, and we can't quite figure out what is missing. When I get into those ruts, which is more often than I'd care to admit, I take on one simple exercise.
What makes this a good exercise? Here's the gist of it. A dream is, quite often, a messy narrative with a lot of inexplicable reality blended into it. Some of it might be wild and outrageous, some of it might be strongly symbolic - it's hard to know what's really in there until you start putting it to the page. And as you do that, a part of you will want to make some sense out of this outlandish set of thoughts and events - especially if you try to write it as a narrative. Your mind will start exploring these weird details and odd symbols, and hopefully wake up your natural creativity.
At this point in writing your dream, you might notice that you are making connections between events you remember and pieces of your actual life. Some might be obvious, others more cryptic, but your writing is starting to try to place dimension and depth into this nonsensical story. In short, the wild collision of neurons firing throughout your brain is being translated - properly or not - into something more real and tangible; something that comes through clearly as a story. At this point, you might be including in your narrative some interpretations of different images and events. This is when your dream starts to take on a life of its own. In short, it takes on the characteristics of something that is not very flat at all.
Often, the missing link in "flat" writing is when the writer is not engaging with any real depth in their writing. They are writing a conversation but it's just explaining the plot and killing time rather than exploring the characters and revealing their pieces. Flat writing is very detached from the writer's deeper feelings, and the reader will pick up on this. To give it some shape, the writer needs to engage with the material on some level, and let themselves feel it on a deeper level. Exploring a dream is a good way to get things moving - it is taking a story our brain told us and digging for meaning and connection that will make it stand out.
Disclaimer: Like all exercises, the final product is quite likely not going to be your best writing. It doesn't have to be. It just has to be the product of doing the exercise and getting your creative workout in. However, if you do get some great short story out of this exercise, dropping me a comment wouldn't be the worst idea.