If a local municipal policeman stops you for speeding how high up the law enforcement food chain do you have to be, to be able to order him not to to give you a ticket?
I would imagine his boss, the local Chief of Police could do this, but who else? Would the State Attorney General or the head of the State Supreme court be able to pull rank and tell him to step off. Could an FBI agent tell him to back off?
Who trumps who in this scenario?
In many American cities, the chief of police is the top uniformed officer of a particular department, and could issue such an order. For that matter, the cop’s watch commander (a captain, lieutenant or even a sergeant, typically) would have the authority to order a subordinate not to write a ticket. But why would any of them want to order one of their cops not to do her job? It could easily be seen as an abuse of authority, or playing favorites (not to say it might not happen sometime, somewhere).
The state attorney general, chief justice of the state supreme court or an FBI agent wouldn’t be in the cop’s chain of command. Each of them could ask, but the officer would be free to ignore them.
Problem in phrasing in your question, I’m afraid.
Joe cannot order Officer Clancy not to give him, Joe, a ticket which Officer Clancy thinks is properly issued. No matter what office he may hold.
Any person who legitimately outranks a policeman may order him not to pursue a given violation – e.g., that he stop running a speed trap, or drop a de minimis charge (57 in a 55 MPH zone, for example, there being no reasons that would make it hazardous).
(Note that members of Congress are immune from arrest or service on non-major charges in their daily rounds during terms of Congress, by constitutional provision – the idea originally having been to protect them from being detained by ‘nuisance suits’ while serving as the people’s representatives. Some states may well have similar provisions.)
As mentioned, you could get a ticket, and be the flipping the President of the USA, and still end up with the ticket, presumably. How you can challenge this later on, is up to you, lot’s of “Joes” have swindled judges into not processing fines, and could even be expunged from your record, I’d imagine.
It should be noted that other people besides police can write you a ticket. I’ve heard firemen, and even postal workers can write you a ticket if need be. Once, my uncle was pulled over for speeding by a reservation fire chief, we were not on the reservation but on public interstate.
My registration expired six days earlier when I got stopped going to pick up my daughter from her new day care. The officer that stopped me said that I couldn’t drive another single inch and my car would have to be towed or impounded at the police station. I explained that I had to get my one year old within the next fifteen minutes no matter what. He said that wasn’t possible and illegal and watched me try to make emergency calls on my cell phone to no avail. There wasn’t anyone else around. He went back to his car and came back a few minutes later stating that the chief of police in Medfield, MA had declared a police emergency on my behalf and that I was allowed to pick up my daughter and drive home as long as I renewed my registration online that night. I didn’t get any tickets and it all worked out well.
Back to the OP, the state police departments have a lot more direct influence than the federal ones like the FBI. It is almost completely jurisdiction specific but the State Troopers have more pull than town police. However, County Sheriffs are often both law enforcement and elected officials and pull strings and make decisions as needed.
I think anyone no matter how far up the chain attempting to stop a ticket being written would be dropping themsleves into a potentially very bad situation in a ‘perverting the course of justice kind of way’ if anyone got wind of it.
In a case in Queensland Australia earlier this year, the Police Commissioner’s driver, with the Commissioner in the car got issued a speeding fine. The Comissioner is the top cop in the state and did nothing. In fact when the media got wind of it, the Commissoner said something to the effect of he was happy the police officer issuing the ticket did his job as he would with any other citizen.
Boss Hogg
Nothing presumable about it - Ulysses Grant got a speeding ticket while in office; the story goes that the policeman didn’t want to issue the ticket when he found out who he’d stopped and Grant insisted he do so.
Uh, speeding what exactly???
Presumably you don’t abuse your power? Presumably they don’t want to write you a ticket cause of your high status and you told them not to? 
A '63 Aston Martin 
A horse-drawn carriage, of course. DC had speeding laws even then.
aawilson I took ‘presumably’ to mean you thought the situation was to date still hypothetical. Sorry.
Quite true. Even more interestingly, it was a black officer. By insisting on the ticket, Grant reinforced both the points that the President isn’t above the law, and that black officers were entitled to the same respect as white officers (not a universally-held view in those days). Good on him.
Old Sam Grant was pretty noted as a horseman, one of those old army officers who took it as a point of pride that he could ride anything on four legs with a snaffle bit. During the Overland Campaign he rode a huge (17 hand) bay gelding named Cincinnati. After the fall of Vicksburg he nearly killed himself when a high strung gift horse fell with him. He was still on crutches when he took over the operations at Chattanooga that fall. He liked big fast horses and he liked to go fast. DC may well have had a “not faster than a trot” ordinance.
Pulitzer Prize-winner MacKinlay Kantor wrote an alternative-history essay, “How the South Won the Civil War,” for Look magazine in 1960. One of the points of divergence was Grant’s being mortally wounded in that accident.