So before you select the fuse you need the requirements for the device you are powering. In this case, it's a 14.4Vdc motor rated at 1.3Amps.(See third picture). Now as I stated in another instructable
The voltage is fixed, the current is maximum needed.
Next you select a power supply that has the same voltage and a current rating higher than the motor (See second picture). As stated in the other Instructable, the voltage is fixed, the current is the maximum the power supply can supply but it will power anything drawing less current.
TIP: Now for the fuse selection. Select a fuse that does not exceed the motor's current rating, 1.3A.
This motor is rated at 1.3Amps. Now if you run it, you will probably measure a lot less. But when in operation, the loading of the motor may change which may increase the current required.
What I would choose is a fuse that's equal to or slightly higher than the motor specification and lower than the power supply current rating. There are two problems. There may not be a 1.3A fuse readily available. Two, DC motors have a surge current when they start up, which could likely exceed the rated 1.3A. That is also why I recommend a slo-blo fuse. They are designed to handle a surge current above their rated value. For this application, I personally would select a 1.5Amp slo-blo fuse.
Selecting a fuse below the power supply rating is preferred as some power supplies may run at their rated capacity but may run very hot and have a shortened life span.
USE: Officially, you should use a 1.3A slo-blo fuse (or smaller if you can't find one).
THe reader may complain that the power supply is 13.8Vdc but the motor is 14.4Vdc. Theoretically, that is a problem but in the real world it is not. Most DC motors will run at less than rated voltages. In fact, this motor is out of a rechargeable drill. The way, they have adjustable speed is by varying the voltage.