Can we use the authentication tag as Nonce / IV for the next message?
The authentication tag in GCM is generated by XORing a block cipher output with the Galois field hash (and truncating it for shorter lengths). It is thus assumed to look PRF. So it is effectively just a random nonce that should not collide until a birthday bound of $2^{t/2}$.

With a tag length of 96 or more bits, it should be secure. Shorter random IV lengths are prohibited in SP 800-38D. However, that standard also limits you to using the key no more than $2^{32}$ times, when using a random IV.

(Even though the nonce is "controllable" by an attacker with a chosen plaintext attack, that does not allow generating a collision except randomly. Otherwise it would lead to a forgery attack.)

I would still prefer a counter.


  For me it looks like it should be safe as the first chunk is standard GCM and every following one is indirectly based on the exact same nonce.


Note that this dependence means two things:


You need the tag from the previous chunk to decrypt the next one, so parallelization is slightly more difficult. (E.g. both processors would need to read the same memory location.)
If some chunk does not authenticate, you cannot trust that it's the only one that has changed. An attacker who changed chunk $i$ could also remove any number of chunks after it without that fact being visible. (With counters you can detect a localized change and still authenticate the rest as being in the correct place.)