Do you need this job? yes or no
Yes > then I'd be careful in negotiations but I'd still try to negotiate that point
No > I'd play hardball with them; no deal under these terms
a few basic questions though no matter your answer above
Did they come to you? did you go to them?
Do you know any other consultants working for this company?
How will this work as far as booking, paying (by who, what CC), who determines when, where, who (airline), routing etc?
Do you use their travel service?
what is the class of service?
do you have to go by their travel policy?
How will ODC reimbursement work?
One way I might negotiate this, is really focus on your consulting rate; then at the end when you give your concessions, use the back door to bring up "if you toss in the FF miles" I'll go down to $NZ rate per hour or are there other t&c's that you could capitulate on that you really do not care about that you could exchange for FF mileage; i'd also negotiate in the bonuses that you will earn; other than base miles I'd give them nothing (if you do go this route) and make them prove you owe them any additional miles. If you toss in EQM or base miles in the contract it may throw them off (I have no idea how FF savvy they are)
another less ethical approach would be to (assuming you use your personal mileage number) is to ask for retroactive credits. i'd be aware as well that they may ask for copies of your statements (FF) later on.
In the end, If I didn't need the gig.. I'd start with the consultant fee/rate; and then say before we get too far, this FF thing has to be resolved as well; if you need it; then its a whole new ball game.. how bad do you need/want the job?
Are you a true consultant? or are you being treated as an employee?
As others have stated, they may have some corp agreement that would cover this including FF miles and corp discount?