I have used Ardex K-15`to level floors. This product allows the addition of pea gravel for filling areas over 1/2" deep. use it with the pea gravel to fill the first 3/4" to 1/2" then use the Ardex K-15 without the pea gravel to top it off.
I guess I got to throw in the obligatory remark, I do not own stock in Ardex, nor do I work for the company. This is a product that I have used before that works supremely when used, following the directions. There is a primer that is used with it.
Edit 2-26-14
When using the primer, lay out how far the Ardex will need to go with a pencil mark to get your floor leveled. read the directions on the primer container for dilution. Spread the primer at least 1-2ft OVER the marks, when feathering, as you will see this will come in handy. This stuff feathers out to zero. Be patient with this. It settles flat over a period of time, 5-10 minutes, you may notice a "ledge" forming at the edge if too much is used. That is where the extra primer comes in.
I forgot to add, you will need to layout two marks, one for the pea gravel added as well. DO NOT get this one too high, 1/8" to 1/4" low so the regular mix will flow over the gravel mix, and not get "hung up". Let it set for 2 hours, then move on with the next step with out the gravel.
Get a container that will allow 2 bags to be mixed at a time. I have gotten it from a big box store, the kind with the rope handles the are about 20 gals +/-. You need it this big to keep the mixing from slinging it out all over the place. Cover the floor where you mix about an 8X8' area aside from where you will pour. The drips from the mixer will be difficult to scrape off after a time
Do not worry about using their mixing paddle, there are paddles that will work.
![paddle1](https://i.stack.imgur.com/BbfAw.jpg)
![paddle2](https://i.stack.imgur.com/S2sIS.png)
![paddle3](https://i.stack.imgur.com/h1X7Y.jpg)
The first one is my preferred one to use, it works with a little in the bucket or 10 inches deep. the third one is second, but it is a glorified whisk, no angles on the blades to "pick up" mix off the bottom. The middle one is an excellent mixer, but only effective when mixing large amounts. The top hoop needs to be covered for this one to work well.
More later if you need it.
Since there will be now way to insure the concrete will be the same color or will it be able to tie in the texture to make the new pour "go away", neatly slope the concrete up towards the post say about a 1/2" to create a break line where the new concrete meets the old. Try to keep the slope uniform from post to post just so it will look professional. The slope will help drainage, even though the concrete acts like a huge sponge, holding moisture to the post, but it is much better than soil.
New concrete can smear over the old making a mess, but after a few hours, you can carefully clean the old concrete with a DAMP stiff bristle brush, no flowing water, taking MUCH care to not let the brush touch the fresh concrete. You may even wait 6 hrs and still accomplish this task.
Best Answer
I'd remove the vinyl. The leveling compound should go on top of the bare concrete.
But before you do anything: check if the foundations are okay. If the floor isn't properly supported, the added weight from the leveling compound will make the floor subside faster.