If you are self-employed and are traveling for business, there is no particular requirement that you travel economically. You can travel first class if you like. The only limitation is on "luxury water travel" (cruises).
Remember though, deducting a big expense instead of a small expense just means you have less profit for other purposes. Suppose that by traveling economy, you expect a total profit of $20,000. After you pay the taxes, you have money left over that you might use to pay for food, housing, clothing, tuition for your kids, or whatever your other needs might be. If you travel first class, you can deduct the expense and then you have an profit of $15,000--even though you can deduct the expense and pay less tax, you still have less money left over for your other living expenses.
If you are a W-2 worker, you can't deduct any travel expenses. Your employer can reimburse you tax-free for any work-related expense that you prove with appropriate documentation such as receipts. Even though your employer could legally reimburse you for first class travel or other perks, they have the option of setting lower reimbursement limits in their travel policies.
