The first thing to check is the diode across the coil. I normally use 1N4004 diodes as replacements (You can find them at Radio Shack if needed). If you can't check it with a VOM just try replacing it. It could also be the coil or more likely the switch contacts. I bought new flipper switches for my old Phoenix from here even though they worked as they were worn and pitted.
Just FYI for your understanding :
Flipper coils are a dual winding coil. The first coil does the big hard kick and then the switch disconnects that coil and connects a lower current coil that lets you hold the flipper in the up position. If it was just a single wound coil holding it up at the higher "kick" current would burn out the coil. Coils are simply big electro-magnets like when you were a kid and wound some wire around a horseshoe bolt and connected it to a battery.