There seem to be a lot of public domain versions of the Flash serials floating around. The DVD’s released by Image in 2000 are what I have and are pretty decent although unrestored. AFAIK, it’s the only release that has the blessing of King Features Syndicate, and is probably a port of the 1996 Laserdisc sets.
http://www.ebay.com/itm/Flash-Gordon-Space-Soldiers-Trip-To-Mars-Conquers-the-Universe-DVD-3-disc-set-/252280071115

I bought the big box of Flash, but you can find the individual serials on Ebay. There are shorter “movie edits” I’ve never seen that have also been released, but probably chop out a lot and you lose the cliffhanger effect of the originals.

Not sure if Buck Rogers is in the same boat, as there are fewer editions of it around. This is what I have, about the same in quality as Flash.
http://www.ebay.com/itm/Buck-Rogers-with-Larry-Crabbe-12-Episodes-DVD-Estate-Listing-/222006409259
Buck initially wasn’t quite as popular as Flash, so Universal only made one serial.

I don’t know if we’re ever going to see an HD release unless somebody pours some money into restoring them. A few Republic Pictures serials have made it to Blu Ray, so anything is possible.