I would like to find out what should be the brazing powder and cycle required to braze a SS 316 honeycomb onto ASTM A516 Grade-70 base material. Is there any additional heat treatment required after brazing?
As far as brazing 316 stainless to A516-70, it should be a very brazeable combination. The 316-stainless should, of course, be the low-carbon grade of that alloy, 316L, so as to minimize any chance for carbide-precipitation during heating or cooling in your brazing furnace.
Post-braze heat treatment of A516-70 should not be required. In the welding industry there are often specification requirements for post-weld heat treatments, but those are primarily for stress relief due to the extreme temperature differentials between the weld pool and the nearby unmelted base-metal during the welding cycle. That does not occur during brazing since the entire part is slowly uniformly heated to brazing temp and back down again whenever a furnace brazing cycle is involved.
Obviously, due to the extended time cycle brought about by any furnace brazing cycle, the base-metals involved typically become annealed, and those properties are what you will have in service following brazing. Thus, be sure that "the yield strength of the base metal in the annealed condition" will meet your needs. If those properties are not sufficient for your needs, then you should work with your steel supplier (or the base-metal manufacturer) to determine if you can increase the base-metal properties by heat treatment to meet those needs. Of course, the strength of the 316L cannot be changed by heat treatment.
By the way, in the latest edition of the AWS Brazing Handbook (published in late 2007) is a lengthy chapter on brazing of honeycomb that I was privileged to produce for that book. In it you will find lots of additional information re. brazing honeycomb to its substrate, including guidelines regarding selection of brazing filler metals (BFM) based on how they can "erode" the thin stainless honeycomb during the brazing process.
So, as far as a particular BFM to use for this braze, you could use any of the standard BNi-XX alloys EXCEPT BNi-6 or 7, since these two contain phosphorus, which should never be used on any ferrous materials. BNi-2 is an excellent choice, but please be aware that it contains both boron and silicon. Both can erode the stainless IF you use too much BFM and then hold it at braze temperature too long. Remember that honeycomb brazing only requires just enough BFM to fill the faying surfaces between the bottom of the honeycomb and the substrate to which it is being joined and also fill the nodes of the honeycomb. When you add all that up, it's a tiny amount of BFM that is needed. People tend to put far too much BFM in the cells for honeycomb brazing, and thus, the excess BFM can eat away the honeycomb. So, keep the quantity of BFM powder that you use to a minimum. An easy way to verify this is to be sure that you can very clearly see almost all of the substrate surface at the bottom of each honeycomb cell when you look at the brazed assembly. The so called "fish-eyes" that some specs talk about are OK, but even there, in my opinion, such an inspection criterion represents the presence of too much BFM.
If for any reason you feel that erosion may be an issue for you, then you might consider moving to the BNi-5 BFM, which contains no boron. It is a much higher melting BFM, however, and higher temperatures can create their own nightmares for some brazing shops.
So, my suggestion is to use BNi-2 (also designated AMS 4777) and to keep the quantity as small as possible. Then, do your normal brazing in a vacuum furnace at about 1950°F (1050°C), holding at that temperature only a few minutes at most and then furnace cool, with no further heat treat needed.
Remember, the honeycomb, being much thinner than the substrate, will come up to temperature much faster than the substrate. Be sure that the heating/cooling rates used are such that you do not cause the rapidly expanding honeycomb to pull away from the substrate (perhaps breaking some of the spot welds holding it to the substrate) when heated or cooled. Depending on the mass of the substrate, some experimentation may be required to find the optimal heating/cooling rates.