How to duct through a new cabinet from a floor vent opening at the wall

You want the shortest distance possible, and for everything except perhaps the dryer connection, you want to use rigid metal tubing rather than the flex tube. The rigid tubing will resist the airflow less and collect less lint. The better airflow from rigid tubing and shortest distance will make the dryer more efficient. If too much lint builds up in the vent, you have a fire hazard in addition to longer drying time.

I'd also suggest having the exhaust somewhere you can reach with a small step ladder to make it easier to clean the vent. So I'd run it down through the floor rather than up through the ceiling, if possible.

Finally, when you install the vent opening in the side of your home, make sure it's weather tight. If it's vinyl siding, you can get a removal tool (it's a flat blade with a hook on the end that pulls two pieces apart). Take off a few pieces where you're working, securely attach the vent, seal around the edges (not sure if Tyvek tape is good enough, they make a rubber adhesive membrane for window openings), install a few pieces of J channel like you have around windows and doors, and cut (measure twice) and reinstall the siding. Vinyl siding screws should remain loose (should be able to slide a fingernail underneath) so that it can expand/contract with heat/cold.

You're mixing grease with lint, which is only going to make a mess and clog up in no time. You could also create a situation where dryer exhaust goes back into your house instead of outside, causing excessive humidity and a mold/mildew risk. The workaround for that would be to install dampers, but those would likely get jammed with the grease/lint combination. And that's assuming that this would be within code, which I suspect it isn't, or every builder would cut the corner. So, in short, my suggestion is that you don't even consider joining the two.

Also, a suggestion, only use flex pipe for the final hookup to each device, and cut away any excess flex tubing. The rest should be rigid metal venting for durability and to give you the best airflow.