Is money earned from buying discounted tickets and submitting invoices for a higher cost permissible or forbidden?

If the company grants you the value of first-class tickets as part of your agreed-upon wage, then this value is yours, and you may travel at any class you wish and keep the difference, unless there is a condition preventing that. However, if the company entrusts you with purchasing first-class tickets, then you are bound by that, and if you purchase tickets of a lower class, you must return the difference.