You can check your spelling in Gmail.
Note: If there are red spell check markings on your Gmail compose text, they are from Chrome's spell check. This can be disabled from Chrome options.
1. Go to your message draft / start composing a new message.
2. Click the arrow icon in the bottom right corner of the compose box. Select Spell check.
You can correct or ignore suggestions on marked words by clicking on them. You can choose another language for the spell check by clicking the arrow icon on the bar which appears after doing the initial check.