When you buy a syringe from a vendor, most vendors attempt to keep the needle as sterile as possible when they create the syringe. When you create the syringe yourself, you also should try to avoid contamination of the needle (which can occur as easily as handling the needle with unclean hands, etc.) Syringes can and do leak as well during shipment through the mails, leading to spore water dripping on the needle and in the needle sheath. That being said, it is probably a good idea to sterilize your needle before inoculation.
Flame sterilizing is just that - applying an open flame to a needle until red hot. This method will kill any spores that may be inside the needle (the 1.5" space between syringe and tip of the needle), so take that into account when inoculating your jars. Flame sterilization also may lead to a char build -up on the needle (a blackening of the metal's surface), which is attributable to using a butane lighter (bic lighters, etc.) The char can be avoided by using a "torch" style lighter. Remember, when using flames, use common sense. The needle will be hot after, don't touch it and let it cool before inoculating.
You should sterilize the needle between each jar. This is advised as it helps stop cross contamination.
After flame sterilising, you can let one or two drops out of the syringe to cool the needle down before inoculation.