Can I attach a kitchen vent and a dryer vent to the same exhaust?
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.