How do I make a GRE tunnel

Make sure you have ip_gre loaded on both instances.

$ sudo modprobe ip_gre
$ lsmod | grep gre
ip_gre                 22432  0
gre                    12989  1 ip_gre

Then on your AWS instance, run the following commands:

$ sudo ip tunnel add gre0 mode gre remote $LINODEIP local $AWSIP ttl 255
$ sudo ip link set gre0 up
$ sudo ip addr add 10.10.10.1/24 dev gre0

We're creating a tunnel device called gre0 here, and tunneling packets will originate from your $AWSIP and flow to $LINODEIP - make sure to change those in the first command.

Confirm it's set up properly:

$ ip route show
default via $AWSIP dev eth0  proto static
10.10.10.0/24 dev gre0  proto kernel  scope link  src 10.10.10.1

Do basically the same thing on your Linode now:

$ sudo ip tunnel add gre0 mode gre remote $AWSIP local $LINODEIP ttl 255
$ sudo ip link set gre0 up
$ sudo ip addr add 10.10.10.2/24 dev gre0

Once that's done, hop back over to your AWS instance and see if you can ping your Linode:

$ ping 10.10.10.2
PING 10.10.10.2 (10.10.10.2) 56(84) bytes of data.
64 bytes from 10.10.10.2: icmp_req=1 ttl=64 time=0.619 ms
64 bytes from 10.10.10.2: icmp_req=2 ttl=64 time=0.496 ms
64 bytes from 10.10.10.2: icmp_req=3 ttl=64 time=0.587 ms