I live in AZ and I was currently in a flex plan with my employer and was laid off in July. The employer (corp in MN) did not have more than 20 employees last year so I am not eligble for COBRA for the remaining balance that is left in the flex account. How can I recop the balance that is left in my account?

I haven't seen your plan documents or SPD, but you should have a period of time during which you can still submit claims for expenses you incurred prior to your termination date. Maybe you purchased some over the counter drugs and medicines, and you can get receipts from many of the retailers like CVS if you used your CVS care card. I think Target can also bring up the purchases if you used a credit or debit card.
Other than that, the use it or lose it will apply, and there is no way that you can get the money back.

Yes I have already sent in all that I can including the expenses that had incurred prior to my termination. I just thought that there would a way to be able to be reimbursed the balance in the account and would receive either a 1099 or it would be paid back to me as a payroll deduction. I had $1162 and submitted $492 so I have a balance left in the account of $670. Being umemployed I could really use this money!

No, you can't recoup it.

But there would be nothing wrong if you could convince your former employer to make a one-time W-2 severance payment of, say, $500.

I don't know the answer to this but does AZ (or MN if you worked there) have a state mini-COBRA law?

Cobra exempt Plans (with fewer than 20 employees) that include Medical FSAs are required to offer Cobra for any employee funded portion of an FSA that involves forfeiture or potential of forfeiture upon termination of an employee's employment.

Cobra exempt organizations who's Employee's Medical FSA claims exeede contributions or will exceede their contributions upon termination of employment are exempt from offering FSA Cobra to only those employees who's claims exceede contributions.

If the organization offers a group health plan and an FSA, the Cobra exception for fewer than 20 employees applies to the group health plan, but not to the portion of of the FSA at risk of forfeiture upon termination of employment.

Organizations that do no meet the Cobra exception must comply with FSA Cobra provisions and Medical Plan Cobra provisions.

Hey, Sieve, you could show some real hubris and suggest that severance payment be $670!

Even $500 might be problematic as an attempt around the use-it-or-lose-it rule if the only one's getting the severance happen to be those who 'forfeited' a flex account balance equal to or greater than, or approximating, their 'severance' pay.

There is that possibility.