The number of emails you can send depends mainly on the limits imposed on your account by AWS SES.
Login to your AWS SES Dashboard and click 'Sending Statistics' in the left pane. You will see something like in the below image. According to this image, AWS has permitted this account to send emails at a maximum rate of 14 emails per second and upto 100000 emails per day.
To prevent abuse AWS gives new accounts a very low sending limit. You can request to increase these limits. They will do so gladly but only if your email sending reputation is good. So make sure you don’t send out any unsolicited emails.
When you send an email campaign, Send With SES tries to send out your mails as fast as your current AWS SES limits allow. Sending emails also depends on your current Send With SES Bill Plan (see below image), irrespective of the limits imposed by AWS SES.