The calculation for linear hashing should be the same as for "non-linear" hashing. With a certain initial number of buckets, uniform distribution of hash values would result in uniform placement. With enough expansions to double the size of the table, each of those values would be randomly split over the larger space via the incremental re-hashing, and new values would also have been distributed over the larger space. Incrementally, each point is equally likely to be at (initial bucket position) and (2x initial bucket position) as the table expands to that length.
There is a paper here which goes into detail about the chain length calculation under different circumstances (not just the average), specifically for linear hashing.