When you say "only a safety chain", I assume you mean in addition to the winch strap (or cable). If you properly pull the boat tight against the bow roller, then the bow eye should be tucked under the bow roller... which keeps the bow of the boat from bouncing.
I subsrcibe to a different school of thought regarding trailer flex. I think it is GOOD that we let it flex. Flex keeps things from breaking. If the boat is tied down so tightly that the flex is eliminated, then that means the energy that would have been absorbed by flexing is transmitted into other parts of the trailer AND also, now transmitted into the boat. Energy has to go somewhere. This isn't really apples to apples, but if you think about skyscaper buildings... initially they were built very rigid and they would end up breaking apart because they didn't flex with the wind. Now, they are built to sway in the wind - often a few feet or more. 'Nother example... large brdiges like the Golden Gate.
Now, I'm certainly not saying there's as much engineering going into a trailer as a skyscraper or a bridge! But "going with the flow" is a good thing. Trying to fight nature is a losing battle.
On the flip side, it can't hurt to have another attachment point as a backup. In this case, I'd recommend using a ratchet strap from the bow eye forward to the winch stand - or at the least, to the base of the winch stand. The bow eye being underneath the bow roller will stop the boat from bouncing - we just need to keep the boat snugged up.
All that said, I am NOT an engineer so don't take this for gospel. But at least give it a good thinking before dismissing it.