What is the best way to move this electrical box a few inches?
If you don't object to having a junction box cover below your new light fixture, consider leaving the original box right where it is. Install the new box above it, and connect the two boxes with a short conduit nipple in a pair of knockouts that line up (or if there's a bit more space than shown, use an offset nipple if that helps to line things up.) 

Wire as needed, put a plain cover on the original box and the light fixture on the new box.

If going with the conduit extension approach, consider an FMC to EMT transition rather than FMC to rigid - a 90 degree EMT bend would do the job nicely from the new box to where the FMC ends, and in general EMT is a lot cheaper than rigid (or flex) even comparing a 4 inch nipple to having to buy a 10 foot stick (though by the time you put connectors on the ends you are closer to the same price, but you have more than 9 feet of EMT left for your next project...

If you don't have a bender or a friend you can borrow one from, you can find pre-bent EMT sweeps to purchase, though they may cost more than 10 feet of straight EMT.