I'm certain neither flue would meet modern safety standards, and that is just from what I can see in that picture with very little information. There are some grandfathering of some issues.
Both flue almost certainly has deteriorated mortar joints or damaged tiles. You would need to have the flue camera inspected(level 2 inspection).
The right flue is fully fucked and should not be used. The tiles are gone and there is masonry that has fallen and is obstructing the flue. Edit: Not a flue, is open chase cavity.
To determine if the flue will be able to have a stainless liner, you need the measurements of the firebox width, depth, and rear wall width. You then can put those measurements into an online calculator to determine liner size. The next problem is how much space you have in the chase(chimney structure surrounding the liner). If your chase has an opening of 10"x10" and you need an 11" liner, that is a problem.
The flue may be able to be coated with a masonry product like Fireguard or Fluesaver. That would depend on the condition of the flue tiles and the exact system used to reline.
The top of the chimney should not be closed off with a cap like you have there. It should have the tiles or a liner extending past the crown(top) of the chimney, the crown would close off the chase and keep water, debris, animals, etc. from being able to enter the chase. Water and products of combustion acting on the mortar joints of tiles and brick will destroy the structure. Just putting that cap on there is better than nothing, but it is more of a way to buy time so you can actually fix it properly. The crown used to be covered and sealed properly, but has deteriorated to the state it is in now.
Get a certified chimney sweep out there for a level 2 inspection of both flue and they will be able to give you a better understanding of what all needs to be done and you can go from there. Use a company that does the inspections and the work. If they don't do the work, then you will have to deal with inaccurate quotes and a bigger headache. Just do an inspection on the right one, no sweep. They should be swept with the inspection to get a good idea of the tile and mortar joint condition.
Edit: fixed some stuff based on further explanation of the situation.
