I'm not sure, but I have found that ProFlex RV sealer to be MUCH stronger and durable than silicone. Not sure of its applicability to your need here as I am not familiar with the installation, but if silicone is a viable option, you may find ProFlex may be a better one.
I would use 3M 5200 adhesive sealant. It is a polyurethane with strong adhesive properties. Nothing is going to stick well to the polyethylene tank, but this product will stick a lot better than silicone.
David
I agree with the last two comments... avoid silicone if you can. They really ought to just give you a gasket since nothing really sticks to the tanks and you're just trying to make it water tight (except things you don't want to stick like poop and toilet paper). Make sure you seal around the screws really well too since those are just as likely to leak as the big hole that you drill.
[font size="3"]I agree on not using silicone. It's not a structural adhesive. Others are better. It would help to know what the "quickie flush" is. What is the physical fitting? How does it attach. I also agree on bonding to polyethylene, but the black tank may be ABS rather than PE. The factory fittings appear to be sealed with something similar to Dicor, Proflex, or 5200. Maybe consult with LL or the tank manufacturer.
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Here's the quickie flush:
http://www.amazon.com/gp/product/B000EDOSME/ref=oh_aui_detailpage_o00_s01?ie=UTF8&psc=1