You'll need a forge capable of reaching forge welding temperatures and you'll need to flux your billets to get them to weld. You might find it easier to simply buy pre-laminated steel.
Good 1084 can make a very nice kitchen knife on its own. I've bought 1084 from a good source in 0.125" thick stock and didn't have problems warping. I've fixed other carbon steel warp by counterbending in clamps during tempering, should work fine with 1084 as well.
You can differentially harden your 1084 by either edge quenching or claying the spine. But even non-differentially hardened monosteel 1084 should be fine a kitchen knife. It's more an issue with swords as it's preferable to have a sword blade be tough and simply bend and be somewhat useful rather than the blade shatter or break and be useless. You're not going to be treating a kitchen knife in the same manner, so it's not a big deal. If you run your 1084 at HRc 63-64 it's not going to shatter but the edge may be a little chippy, something that wouldn't be changed by cladding anyhow.
Edited to add: One advantage of cladding is if you clad a carbon core with a stainless cladding. That can make for easier maintenance as the cladding will be stain resistant.