Yeah, we definitely need more info on what you've built. A screenshot, if nothing else.
But if I'm reading your post right, you're not seeing any mobs, so I'm going to outline the reasons why you might not be seeing any spawns whatsoever, as that's a lot simpler.
First, to state the very obvious (but I've made this mistake in testing worlds more than once), is your world on Peaceful difficulty? :-)
Since you've built up in the sky, are you sure your platforms are completely dark? Unless it's completely enclosed (solid roof + walls), you'll need a bigger roof than you think, since the sunlight will spread. Mobs will spawn at light level 7 and below (check the block light level with F3 when you're standing on the spawning platform(s)), but you'll get much better rates at light level 0. Although that may seem obvious, it can be easy to forget when you're worrying about all the other considerations of how to kill the mobs, transport their items, decorate the build, etc.
Next is distance, as TheWesson pointed out. You need to be at least 24 blocks from your spawning platform (each block on the platform), or no mobs will spawn. At 32 blocks, mobs won't move on their own (so you'd need to use an automated design such as a flushing water farm), and you can get random despawns (but that isn't always a big deal). At 128 blocks, though, hostile mobs will despawn.
Next, are your spawning platforms built out of solid, opaque blocks such as cobblestone? You can use slabs, but if you do, you must use top slabs. Mobs will not spawn on bottom slabs, stairs, transparent blocks like glass or leaves, and a few others. Best bet is to stick with something cheap like stone or dirt. They also won't spawn on trapdoors, carpets, doors, and most other non-fullblocks that have a hitbox (and some that don't). Again, if you just build with basic blocks, you should be fine. Also make sure that there is at least a 2-high air gap to the ceiling, or 3-high if you want Endermen.
Next is the hostile mob spawn cap. This depends on the number of loaded chunks, plus a border, for each player online in the same dimension (overworld, nether, or end). In singleplayer at default render distance the cap is 70, meaning once there are 70 hostile mobs in the world, no more will spawn naturally. It would be higher with more players elsewhere in the same dimension. If you are seeing some mobs on your platforms but very few, and the light level of every spawning space is 0, then it's an issue with the mob cap. The solution to this is to prevent spawns within 128 blocks of your AFK spot, by lighting up the surface, underground caves, moving your farm higher in the sky, whatever you need to do, and, secondarily, to make sure you kill any mobs that do spawn as quickly as possible, as they will count towards the cap until a second after they die. I guess if your platforms are incredibly small, that would also limit the rates, but in practice, even 16x16 platforms can produce a decent amount of mobs.