Are you looking for non-motorised routes, then? NCR 33 Festival Way between Nailsea and Bristol isn't completely flat but only has a few rolling climbs around Long Ashton IIRC, if you follow the bypass instead of going through Ashton Court (I forget which is the signposted route now). Then I think that also gives access to the Portway cycle route, the Frome Greenway, Bristol and Bath Railway and Malago Greenway, but bits of back road and cycle lane have to be used to connect them.
If you don't mind mostly-quiet roads then the rest of NCR 26 (Strawberry Line) to Clevedon and then 410 to Pill is pretty flat, or the other way to Cheddar; plus the rest of nearby 33 and 3 until you get to Wells I think are also quite flat. As are almost all the back roads between Brean/Bleadon, Bridgwater and Wedmore, except for the obvious hills that you can see coming.