If you move files from an infected machine to a Wi-Fi Cloud storage, then move the same files from the Wi-Fi storage to a non infected machine, could you infect your new non infected machine?
If you copy an infected file from an infected machine to a cloud service, then copy it to the new (clean) machine, it will not automatically become infected. It will only be infected again if the user opens one of the infected files.
I recommend ensuring that you do not copy any exe, dll, sys, scr, bat, pif, lnk, com, or other executable files over. You can also do a malware scan of the disk after you copy files over in order to detect the malware on disk in case you copied it accidentally, in order to minimise the probability that you re-infect the machine. You should also ensure that all software on the new machine is fully up to date (particularly Windows Update).