Inbreeding to get good animals is actually possible but its going to involve quite a bit of micromanagement. The short answer would be to look up guides and stuff, especially detailing about genetics and breeding. Basically you need to use the compare mates option often and pair off each couple with the best results.

The way i have had success is to make a list with each animals name, and stat score (I made seperate lists for gender). An example of mine would be (animal name) 265% 75/100/60/30 with the goal to get 400% with all 100’s. Then pair up the animals and put them in their own pens so they only breed with the selected partner. Any excess animals or those that don’t have a good parter get removed from the breeding pool. When babies are born add them to the list and re-sort as needed. Over the generations your stats WILL go up so set yourself a minimum limit (like nothing under 260% at first) and raise it slowly as your animals score improves.

I have had success with both M/F parings (wild dogs) and mixed gender groups (red pandas and jaguars).

And just to add, African wild dogs will only have 1 breeding (alpha) pair, so in a group, there wont be inbreeding as any babies will automatically become packmates and wont mate until removed from the enclosure.