Is there any advantage to incubating an egg with the infinite use incubator, or the limited uses incubators? Are CP values or rarity of the hatched pokemon affected by the type of incubator used?
There is no difference between hatching with each incubator.
However, if you want to get the most out of your temporary incubators, it is recommended that you try to only hatch 10km or 5km eggs in the temporary ones (preferring 10km). Doing this will allow you to be hatching more eggs at a time.
No, there is no indication of different results using different incubators.
I don't think there is any difference! Although I see a lot of people saying they do not like 2km eggs. Here is a bit of info for you: yesterday my boyfriend offered to walk around the block to hatch my 2km egg and he waiting for me to crack it open (I didn't want to walk anymore we had just went for a 10km walk for a different egg) Well as that 10km only got me a Zubat, the 2km gave me a Pikachu. I was very very very surprised and excited. I used my infinite use on the 2km and the limited use on the 10km. It is purely just luck everyone!! ☺️
I'm late to this conversation. I think the best is to use infinite use incubator for 2km or the shortest distance eggs you have on hand and use limited use incubators for 10km or the longer distance eggs you have on hand. Let say you have one 2km egg and one 10km egg with one infinite incubator and one limited use incubator with one use left. If you put the 10km in the infinite incubator, after the 2km egg hatched and limited use incubator is used up, you'll have to wait until the 10km egg hatched to free up the infinite incubator unless you buy more incubators. While the vice versa will free up your infinite incubator quickly for the next egg.
The best use for a limited use is for a 10k egg. This is because you can then hatch your smaller eggs while waiting for your 10k egg to hatch at the same time.