When on the page for enlisting a new pilot, you can see what planes are available at the time you start a campaign.
Also, if you go into manual deployment you can select individual squadrons and there is a list of the planes they will fly over time. To see when they arrive you have to adjust the time (scroll through various week, month, or year selections for the new pilot) which is a bit fiddly but works.
E.g. In the pic above I just found out that Jasta 1 is stuck with the Aviatik B1 until October 1915, and then the Aviatik C1 shows up.