Regarding plastic syringes, they are washable and plain hot tap water will do the trick for nic base, PG, and VG. For flavorings, I suppose it depends just how meticulous and precise you want to be. A hot water rinse between flavors probably removes at least 99% of the old flavor, but if you are a perfectionist, or just don't want to deal with rinsing during your mixing process, separate ones for each flavor might be what you want.
Regarding the needles, most of what comes in contact with your fluids is metal, so I would be even less worried about "cross contamination" with a quick rinse, and perhaps wipe down the outside with a paper towel and blow out any water from the inside before moving to the next flavor.
You can reuse the disposable plastic syringes and needles many times, but the markings may come off the syringes from washing. Clear tape or clear nail polish on the outside will preserve the markings. I am biased against nail polish so it is tape for me, but others use it with no apparent problems. Danny's recommendation for dipping the rubber part of the plunger in VG is also good.