The walk to DHS from Boardwalk or the S/D is about 20 mins. Add a few mins to that for YC/BC...maybe about 25 mins total.
To get to Epcot, walking, takes about 12 mins from S/D, 8 mins from BW, and about 8 from YC and 6 from BC...depending on where you are at the resort.
You can also take the boat....from Epcot to DHS, by boat, is 25 mins. The boat leaves Epcot, then goes to BW, then YC/BC, finally to S/D and on to DHS. Returning to Epcot from DHS, the boat stops at S/D, then YC/BC, then BW and finally gets to Epcot.
Walking is almost always faster. I have left the boat area at the exact same time as the boat....we tried to get to the boat before they closed the ramps, but we were a min too late....the CMs on the boat told us another would be along in 15 mins. Nope, we yelled...we would walk...and we would beat them to DHS. No way, was the response. Well, they did beat us to BW, by about a minute....but the last we saw of the boat until we got to DHS, was as it made it's way to YC/BC. We finally saw it again, coming around the corner as we went to bag check at DHS...they were about 8 mins behind us!!! Too funny.
And if there isn't a boat right there, or coming in, you could face a wait of up to 20 mins.
So....there you have it. Probably more info than you needed or wanted.