Is there a reference that prove that the AES Key Schedule generate random looking round keys? Starting from uniformly random generated AES master key, is there a reference that prove that an specific roundkey can be considered as uniformly random generated as well ?
Actually, that's remarkably easy to show.  The AES key scheduling logic is invertible:


For AES-128, you can start at any round, take a specific setting for that round key, and invert it to come up with the unique AES key that generates that round key
For AES-192, you can start at any round, take a specific setting for that round key (and 64 bits from the previous or next round), and invert it to come up with the unique AES key that generates those round key bits
For AES-256, you can start at any round, take a specific setting for that round key (and the 128 bits from the previous or next round), and invert it to come up with the unique AES key that generates those round key bits


Because that is a 1:1 mapping because the master key, and the 128/192/256 round key bits, then if the master key is selected uniformly, so must the round key bits be.