I've tried to find an answer to your problem online but, alas, without success. However I'm baffled as to why you're using Chrome anyway. Webmail has always been a 'second best' way of accessing an email account, as email was invented on the assumption that people would use a dedicated email client to send and receive mail. For example, if you walk into almost any office in the land, you'll find that the business emails are all dealt with using the program (rather than the website) called Outlook; businesses don't log into websites to send and receive their mail.
So if you're using an Android phone, instead of a computer, it makes far more sense to use a dedicated email app than to have to open a browser and load a website. As you're using Outlook.com as your email provider, it would seem to make most sense to me to use the Outlook app to access your mail:
https://play.google.com/store/apps/details?id=com.microsoft.office.outlook&hl=en_GB&gl=US
Then you'll always be signed into your email account.