This is my first year for this client.   On prior year return, since the mileage was an out-of-pocket expense, it was recorded as an increase to the capital account along with the deduction.

So Debit Mileage Reimbursement, Credit Capital account. OK. That's fine. 

However, it was not recorded as an increase to partnership basis on the basis worksheet........I'm thinking that it should also be recorded as an increase to basis.

You would increase basis (b/c of the credit to the capital account)...but then guess what an expense does to partner's basis? You got it! It reduces basis. Sounds like a wash to me.