Setting up an Office 365 account in the native iOS Mail app takes a few steps:
On your device, go to Settings > (scroll down a little) Accounts & Passwords > Add Account.
When the list appears, choose Exchange:
On the following screen, enter your email address and a description of your account and tap Next in the top right.
A dialog box will pop up confirming you want to sign in to your Exchange account. Tap on Sign In.
On the next screen, enter the password for your email account and tap on Sign In/Next.
If the next screen is asking for permissions for Mail, allow them and tap Accept.
On the last screen, you'll see a list of items you can sync with your account:
Enable Mail, Contacts and Calendars here and tap Save. It can take a little while if you have a large mailbox but messages should start coming in to the iOS Mail App.