I am working on designing a set of gears for 3D printing. I have not done any gear design before - how should I improve the design to prevent gear slipping?
Teeth on gears generally will not slip if your pitch and tooth profiles match properly, since the teeth would have to break off to slip. Minimizing backlash can be done by tight tolerance control.
Looking at the images you have it appears as though you've designed the teeth more freeform and by eye, rather than calculating the profiles (I could be wrong though). If you're working through CAD to completely design the gears, you can write a macro that will generate profiles based on any tooth profile.
The general process for this is create your drive gear however you like. Then create an idler gear with no tooth profile at all overlapping the drive gear. Subtract the interferance between the two parts from the idler, then rotate each based on your prescribed gear ratio. (how much you rotate each will depend on how accurate you need you profile to be). Repeat until you've completed one full rotation of whichever gear you're trying to make. - basic youtube video of how it works here https://www.youtube.com/watch?v=9MycFQKnZkA
Or you can go the pure math method of designing the gear tooth profile completely through mathematics. Which is much more complicated.
Easier still, use off the shelf gears!
In gear design, the most used tooth profile is the involute profile. I am not sure what do you mean by avoiding slipping(Velocity of sliding) because for two gears to move, there will definitely be slip as they have to maintain the contact while they transmit motion(except at the pitch point).
Since you are using a 3D printer, please use the cycloidal profile as a tooth profile which rolls without slipping. The reason people don't use it is the difficulty in mass manufacturing.(Although they are used in clocks and watches)