When creating LoadBalancer service (which will create an actual load balancer), you can now specify preallocated Elastic IPs by id via annotations.

Example:

apiVersion: v1
kind: Service
metadata:
  name: some-name
  annotations:
    # only network load balancer supports static IP
    service.beta.kubernetes.io/aws-load-balancer-type: nlb
    # comma-separated list of Elastic IP ids
    # the length of the list must be equal to the number of subnets
    service.beta.kubernetes.io/aws-load-balancer-eip-allocations: eipalloc-abcd0000,eipalloc-abcd0001,eipalloc-abcd0002
  ...
spec:
  type: LoadBalancer
  ...

Assigning Static IP Address to AWS Load Balancer

The answer to this post still rings true in this case.

The way Amazon does load balancing is it will scale up and down interfaces as needed to handle the request load. This is why they assign you a domain name instead of an IP address since your load balancer could have multiple physical interfaces and the IP addresses will frequently change.

If all you are trying to do is create a DNS name for your load balancer, this can simply be done with any DNS provider by creating a CNAME record pointing to the dns name of the load balancer provisioned by AWS. If you are using Route53, it is even simpler since you can just create an A record with an alias to the DNS name.

I hope this helps. FWIW, it is not possible to get a single static IP address for your load balancer unless you are only deploying it in one Availability Zone.

You can provision the Elastic IP on AWS and configure the service with that IP.

Ex:
type: LoadBalancer 
loadBalancerIP: xxxxx