So, what happens if Hess's mission to Britain is successful. His 'peace mission' is met with interest in a disheartened Britain. In a Britain at that time doesn't know where good news could come from.
Churchill would be fervently opposed to any rapprochement with Germany, but suppose (however unlikely) he was out-voted.
What sort of 'peace' could have ensued. Peace was more to Germany's advantage than Britain's, so Germany could be generous.
It may be as little as cessation of hostilities, ending the blockade, trade, with a view to exchange of prisoners.
Personally I think it very unlikely, on the other hand - not impossible - OTL unlikely things did happen. So, given that it did, what else happens:
- Hitler happy - Stalin not, nor FDR - but more detail ??