So I figured out the real problem is that I created a build using mysql_ram_disk instead of mysql_dsn in amp config- meaning the mysql database is in RAM, and of course disappears when I turn off my laptop :) .
It's a little bit hard to answer without more info but generally the ram disk isn't going to save your data unless you do something extra, so it's more useful for one-off tests or something where you need speed over permanence, like running unit tests (which it mentions in the readme). I don't use buildkit since I'm on windows but I do switch over to a ...
I encountered the same error, setting up buildkit and then running amp config and amp test on Ubuntu 19.04.
What I figured out was that I too had initially chosen 0 for perm_type when running amp config.
I changed the perm_type value to linuxAcl and chose www-data as the web user.
Using those values then allowed me to successfully run amp test.
So, duh. I haven't totally figured out the problem - now I'm getting this -
SQLSTATE[HY000]  Connection refused
but the Access denied issue was a simple fix, i.e., use chmod.
See "How to Run MySQL as a Normal User" at https://dev.mysql.com/doc/refman/5.7/en/changing-mysql-user.html .