You can get burner like functionality in ProtonMail by using a custom sieve filter, and catch-all email — here is how.
Importing emails to ProtonMail
I recently signed up with ProtonMail — I wanted something secure, able to handle PGP encryption and with a nice webmail interface and Android app. After giving the free account a quick look, I upgraded to a paid account and moved two custom domains over. Everything was going great. Time to import my decade of emails into my ProtonMail account…