Can you file a 1096 form with your 1040a?

Are you asking about a 2017 tax return or a 2018 tax return? Form 1040A no longer exists for 2018 tax returns.

See this prior answer regarding filing form 1096 with a W-2G: https://ttlc.intuit.com/questions/3906959-on-my-w-2g-form-it-mentions-to-file-with-form-1096

For tax year 2018 you will need Deluxe or higher to report gambling winnings on a W-2G when using the online product. It is entered on the new Schedule 1 and flows to the new form 1040. 

You can use any version of the CD/download product to report gambling winnings.