I wanted some clarification on this.

I work at a major retail chain.
I voluntarily transferred to a new store. I moved from Ohio to Florida. Can I claim moving expenses for this?

Yes - the move was work-related and was more than 50 miles, so you may deduct expenses as long as you work at least 39 weeks in your new location. For expenses you may deduct see:
Tax Topics - Topic 455 Moving Expenses

You can also claim the moving costs if you got reimbursed for your costs, but the reimbursement was added to your taxable wages/salary.

The only time you CANNOT claim moving costs on a job-related move is if the reimbursement is completely NON-taxable. That DOES happen, but it is rare.