How long to wait to feed hashing using SHA 256? I have a source which generates secrets at $8-10 bits $ per second. I need to use this secret to feed another generator every second. I am wondering how long should I wait while I am concatenating 8 bits every second and then use longer bits as input to hash.

I have two options:


Use 8 bit that I get every second, hash it and send to next level every second.
Wait for say 10 seconds then hash the final say 100 bit. In between for 9 seconds keep sending hashed value of previous 100 bit using public informations.


Which one is more secure?
I am using HKDF for hashing.
You should aggregate bits until you have enough seed bits to start your DRBG using an initial seed. Your seed should contain at least 128 bits of entropy (the amount of uncertainty to an attacker).

Then you could either add the bits as additional seed when you get it or you could first aggregate some entropy. With only an update rate of about 8 bits per second you might as well directly add the entropy to your DRBG. 



To create the same pseudorandom bit stream on both sides you should:


make sure you got the same algorithm on both sides;
configure the DRBG identically on both sides;
update your entropy at exactly the same time;
request data from the DRBG using the same methods and parameters.




Note that HKDF is not a pseudo random number generator (PRNG) or deterministic random bit generator (DRBG, same thing). It may be a pseudo random function but that's not the same.

HKDF turns an already secure key into more key material, possibly given additional information. HKDF / HMAC could be used to build a deterministic random bit generator. If you want to do that then you need to create a paper and prove it is correct.

I would recommend having a look at NIST SP 800-90A (revision 1) and pick a DRBG from there.