As Applespider says, I think avoiding hills in this part of London is a pipe dream!

The only "off road" way I know of to get to Dulwich Park involved going through the woods (which you can get to off London Road just after the junction with Sydenham Hill - it's signposted for the green chain walk) but I don't think you're allowed to ride your bike in there (and it would need to be a mountain bike anyway) - it's a lovely walk though (albeit a much longer way to get to DP than walking the roads)...