How do we reboot in Test Kitchen using cookbook and post reboot, continue the cookbook testing on Linux platform?
How to use Test Kitchen to simulate a reboot on the Linux system?

Test Kitchen is used to automatically test cookbook data across any combination of platforms and test suites.

This scenario entails reboot using the Test Kitchen, followed by starting the chef client post reboot. Additionally, validation should be in place to prevent the reboot from occurring again.
This is merely an example and idea; it can be tailored to your individual needs and desired outcomes.
There are 2 options listed either using one time service or using cron job. Both the recipe's are listed.

The defining about reboot needs to be listed in the kitchen.yml. The specific error code indicates about the reboot which is scheduled and the wait time for retrying. These are listed in the provisioners as below.
Part of the kitchen.yml about the provisioners details is as listed.

provisioner:
  name: chef_infra
  product_name: chef
  chef_license: accept-no-persist

 # Allow reboots
  retry_on_exit: 2
  wait_for_retry: 200
  retry_on_exit_code: # An array of exit codes that kitchen should retry.
        - 35              # Reboot is scheduled

Cron Job
The following is the cookbook recipe using CRON for the reboot and validation in place.

Recipe

# This is the reboot with nothing as action
reboot 'now' do
  action :nothing
  reason 'Cannot continue Chef run without a reboot.'
  delay_mins 1
end

# This will create a cron entry for reboot now, with the condition if file does not exist.
cron 'Reboot_entry' do
  command 'opt/chef/bin/chef-client'
  time :reboot
  not_if { ::File.exist?('/var/tmp/result.txt') }
  notifies :reboot_now, 'reboot[now]', :immediately
end

# This creates a file just a validation about reboot.
file '/var/tmp/result.txt' do
  content 'This records the server will be rebooted'
end

# Removing the cron job if the file exists.
execute 'remove cron' do
  command 'crontab -u root -r | grep -v "Reboot_entry" | crontab -u root -'
only_if { ::File.exist?('/var/tmp/result.txt') }
end

One Time Service
The alternate options like using one-time service in Linux for rebooting the server. This below code, creates an on-time service for the chef client using the template. Reboots the machine and the one time service created will run the chef client and do its tasks.
 

Chef Template - onetime.service.erb

Description=one time service for CHEF Client run
[Service]
ExecStart=/opt/chef/bin/chef-client
[Install]
WantedBy=multi-user.target

Recipe

# Create one-time.service unit file from template
 template '/etc/systemd/system/onetime.service' do
 source 'onetime.service.erb'
 mode '0644'
 not_if { ::File.exist?('/var/tmp/result.txt') }
 notifies :run, 'bash[chef client scheduler]', :immediately
 end

# Schedule the reboot using systemd and enable the one-time service
 bash 'chef client scheduler' do
 cwd '/tmp'
 code <<-EOH
 systemctl daemon-reload
 systemctl enable onetime.service
 EOH
 action :nothing
 notifies :reboot_now, 'reboot[now]', :immediately
 end

# Reboot 
 reboot 'now' do
   action :nothing
   reason 'Cannot continue Chef run without a reboot.'
   delay_mins 1
 end

# Validation
 file '/var/tmp/result.txt' do
   content 'This is post reboot of the server'
 end

Please refer below links for more details. 
Test Kitchen  - https://kitchen.ci
Error codes - https://docs.chef.io/workstation/config_yml_kitchen/