The recommended and supported way to upgrade your AWS Beanstalk environment is documented here and managed platform updates are discussed here, honestly I'd stick to that if you want things to be easy (and that's what Beanstalk is all about), you'll theoretically only get the non-breaking updates and AWS will manage the process so there's no downtime.
So I just want to reiterate that managed platform updates are probably what you or anyone else coming here from Google will want, but if you want to know the latest AWS provided AMI for your Beanstalk environment it can be done fairly trivially with AWS CLI (thanks to sane naming conventions from Amazon on their AMIs).
Starting with an instance from your environment, describe the instance to get the current AMI (skip if you already know the current AMI).
aws ec2 describe-instances --instance-ids i-0909613f35ec0ffee --query 'Reservations[*].Instances[*].ImageId' --output text
Take the resulting AMI ID and describe it.
aws ec2 describe-images --image-ids ami-35290a56 --query 'Images[*][Architecture, Hypervisor, Name, RootDeviceType, VirtualizationType]' --output json
We can use the output of the above as input to a new, sorted
describe-images but this time we replace the timestamps with
* wildcard symbols, like so:
aws ec2 describe-images --filters 'Name=architecture,Values=x86_64' 'Name=virtualization-type,Values=hvm' 'Name=owner-alias,Values=amazon' 'Name=name,Values=aws-elasticbeanstalk-amzn-*.x86_64-python34-hvm-*' --query 'sort_by(Images[*], &Name)[-1].ImageId' --output text
Due to the power of lexical sorting and ISO 8601, we end up with the latest AMI, which in my example is
aws ec2 describe-images --image-ids ami-1be5de78 --query 'Images[*].Name' --output text
Again, I wouldn't recommend you try to change to this AMI by hand, Beanstalk has provisions to do all this for you!