Authenticated encryption and file data integrity
the IVs of next blocks are going to be extracted from previous block ciphertext.


Here assuming chunks since CBC requires IV only once per message/chunk.

IV of CBC should be unpredictable, i.e random. It is not a good idea to extract from a known source. Use randomly generated per chunk.


  First option


Enables chaining, you should also add the IV with the ciphertext. You can store the last HMAC since you can generate from the beginning. As you said this prevents the detection of chunks that have errors during transmission. This can cause re-transmit all the chunks. 


  Second option


There is an attack on this case. If the same key is used for different messages, and an attacker may replace one chunk with a chunk from an old message and you cannot notice this attack if there is no validation for the message. 

Better solution

Use chaining and send the intermediate HMAC results, too. This is actually combing of first and second. It enables to detection of the errored chunks and prevents the replacing attack on the second option.