I haven't used latex, but I have done something similar with silicone rubber. It's pretty straight forward. Depending on how complex your swirl is, making the mold could be complicated.
I used 1/16" laser cut craft plywood to make my postives. I tried balsa at first, but it was too fragile and the grain was coarse. That made it hard to get the finish I needed.
I sanded the plywood pieces to get the contours I wanted and gave them several coats of gesso. I sanded the gesso to 400 grit. Then gave them a couple coats of acrylic auto body primer. I sanded that down to 1000 grit and polished with a finishing pad to get a near mirror finish.
I used wood glue to attach the positives to a piece of foam core and used a strip of foam core and hot-glue to build a box around it. The easy way to build the box is to cut the strip to the length of the perimeter of the box, then cut one side of paper at the corners and bend each to 90°. That way you only have to seal one vertical seam with hot glue.
If you use hot-glue to attach the positives to the foam core, make sure they are flush against the foam and the hot glue hasn't created any stand-off under the pieces. If they aren't attached flush to the foam, the rubber will spread under the positives and create a lip in your mold. That's a mess. That's why I used wood glue. It's easier to get flush than hot glue is.
If you make your pattern as a negative, you're ready to pour your sheet. If your pattern is a positive, like mine, you'll have to make a negative mold. Just pour a mold rubber into the foam core box, wait for it to cure fully and tear the box away. Now you can pour your sheet in the negative mold.
I used Smooth-On Dragon Skin 20 for the mold and the casting. Silicone and latex will stick to themselves, so you have to use a mold release. For casting silicone on silicone, I use Mann's Ease Release 200. Spray a thin coat onto the mold and brush the entire surface lightly with a soft brush. That ensures a uniform coating. Then spray another light coat and let dry 30 minutes.
You do have to be careful about
cure inhibition. Some substances will cause the silicone or latex to fail to vulcanize. The result is a slimy mess. Sulfur is hell on silicone, so don't use sulfur based clay for the pattern. Tin cured silicone can inhibit platinum cured and there many other common household substances that can cause inhibition.
I've never had a problem with wood glue, hot glue, foam core or primer. You should test your materials together to make sure they are compatible.
When mixing and pouring the rubber for your sheet you have to be careful to avoid trapping air that will cause bubbles in your casting. Don't whip the rubbers when mixing parts A and B. Just stir thoroughly and make sure to scrape the bottoms and sides.
If your using a thick rubber, you might have to degas the rubber after mixing. That requires a vacuum degassing chamber ($$$). Alternatively, you can use a thin rubber that won't trap air. Dragon Skin NV (no vacuum) would work for that.
To pour, you want your mold to be level. That will ensure the casting has a uniform thickness. My work bench is slightly tilted so I put the mold on a board and use a couple shims to level it.
Slowly pour the rubber from as high as you can manage. The stream should narrow down to almost needle fine before it hits the mold. This helps force out any remaining air. Pour the rubber into a corner of the mold and let it flow around and over the pattern. This again helps minimize trapped air.
As the rubber cures, small bubbles might rise to the surface. That might not be a problem, since this will be the back of the sheet. If you need the back to be smooth, gently blow on the bubbles with a hair dryer or a heat gun set to low. Don't use high heat or air flow. Just enough to pop the bubbles before the rubber cures.
My pieces were small, but they came out great. Just had to trim a little bit of flashing off them. I've played around with some bigger sheets. The technique seems to scale well.