Rather you than me when it comes to canoeing on the Severn Estuary. I'm sure it's been done, but as a novice kayaker I certainly wouldn't. There are some vicious tidal currents, and I suspect your chances of ending up where you want to be a quite low and where you don't want to be quite high.
Concerning the Slimbridge Swamp tile: it has been done by at least one person but I suspect that this was some time ago. Google maps shows an inviting track at Purton leading in the right direction: nowadays this has a locked gate with barbed wire over it. The same for the track from the Slimbridge side. On land, this leaves access from the canal: I suppose this could be done but would involve fording drainage ditches and forcing your way through hedges. On water a quick paddle from Purton at slack water may be possible, but as I said above: rather you than me.