Congratulations on your acquisition of a classic.
IMO, the best way to establish the basic health of the amp is to get a variac, adjust the variac so that you can measure 117VAC across the power transformer primary, and then take measurements at the circuit nodes listed in the chart in the assembly manual.
But, since you’ve noticed a problem, it would be good to address that first. If one of the 15.6 ohm "biaset" resistors is really burned, it is from excessive current flowing through it from one or both of the power tubes in that channel, though it would be quite a meltdown. The excessive current could be due to more than one cause, including a fault in the biasing circuit or a bad tube.
There are a couple of things to look for that could affect the proper operation of the bias circuit.
With the EL34s out of their sockets, measure directly across the 1000 ohm resistor at pin 5 of both sockets to make sure they are not open. That is, both sockets in the channel with the burned biaset resistor.
Then, I’d painstakingly clean the octal socket contacts (interdental brush, 99% isopropyl, blow out immediately with compressed air), with special emphasis on socket contact #5 in all four of the EL34 sockets (poor contact at #5 would cause a problem with the bias).
Next, retensioning contact #5 in all four EL34 sockets is important. You need to find some kind of tool(s) to slip into the socket from the top and press onto the side(s) of the contact to close it up a bit - but not too much or you won't be able to get the tubes back in. I’ve used an awl-like tool for this, but whatever works.
The contacts I've thus far seen in original Dynaco sockets look kind of like the letter "C" from the top. If yours are also like this, then when retensioning them I’d suggest pressing on the "top" and/or "bottom" to try and close the split in the "C" a bit, if you see what I am getting at. I would avoid pressing the one side directly opposite the split, as this might open the split more.
All of this should be done with power off, unplugged, of course. Being familiar with safe work practices around high voltages is essential.
There may be other causes of the burned resistor, but cleaning and retensioning the socket contacts is important, regardless, especially in an older amp. Perhaps a new set of tubes may be in order, or a coupling cap on the PC board may be bad. You may want a new biaset resistor to replace the burned one - I believe Kevin Devaney at dynakitparts.com sells new ones.