When entering Process content spelling mistakes may not be picked up by the spell checker

Nintex Promapp doesn't have its own spell checker, this is controlled by browser behaviour.  

Chrome or Firefox:

Check the browsers language and spell check settings

Internet Explorer or Edge:

Check Windows operating system spell check settings.  The setting is found in Settings > Devices > Typing.
 

You may need to contact your IT team if these settings are restricted in your organisation.