Let’s say is a relatively modern prison. Do the cells unlock to allow inmates to escape the flames? Or do they lock down give the chance that prisoners might be roasted in their cells?
I’m guessing with some prisons there are large open-air but fenced areas like an exercise yard they could let the inmates go to that would be reasonably far from flames.
Something like a barbecue pit? 
If it’s a modern prison, it’s a fully sprinkled building with adequate smoke and fire separating walls and doors. There wouldn’t be a large fire, the building will control the fire before human intervention can begin. Also, there are very few materials in prisons that support combustion.
Inmates close to the area of origin would be moved elsewhere.
The fire and building codes to build a correctional facility are surprisingly restrictive.
First, its very difficult nowadays to set a modern prison ablaze - the wings are comprehensively subdivided so that spread is very limited. An individual cell and its occupant might burn but not the whole unit.
Materials such as mattresses, furniture etc are all fire resistant, there are plenty of fire detectors too, and a number of automated fire control systems, such as hand actuated sprinklers, and misting systems.
This means that large fires during lock down periods such as nights and other low staffing levels are unlikely.
You’ll not be too surprised to know that the threat of fire is taken extremely seriously. in some prisons, neither staff nor prisoners are allowed any smoking materials, this has reduced the outbreak of smaller fires by around 80%.
All the accommodation unit staff have various drills and routines in the event of a fire, however this will likely occur during serious disturbances, and usually most prisoners actually want nothing to do with it. We have evacuation plans, structures to move prisoners in specific numbers to specific safe locations.
The really dangerous prisons are the ones with large enclosed accommodation spaces, instead of individual cells - when fire breaks out in or around these, then large numbers of fatalities are possible - I have seen a number of overcrowded US facilities on tv where prisoners are housed on litters in gymnasium sized rooms.
Its not a great idea to have large numbers on one space anyway, you get a certain dynamic that makes incidents much more likely, and that’s when you can get fires. The US overcrowd model presents huge risks on control and order, despite the availability of armed spotters.
I did quite a lot of work analysing the figures, and unless you ban all naked sources of ignition, such as cigarettes, you really have to rely on training your staff, and having sufficient numbers of them. Poor prison unit construction and over crowding are the main features of all these events.
If it goes wrong, well you can imagine,
Can you go on about what that dynamic is?
I took the 10 hour OSHA class a couple of weeks ago, and one thing that came up was that prisons are among the few workplaces where you are allowed to have exit doors that are locked to the inside (that is, doors that prevent someone from exiting). The caveat to this is that prisons are under active supervision 24/7, unlike many workplaces, so the guards would be responsible for guaranteeing the safe evacuation of any prisoners placed at risk.
Is it not the case that in most modern prisons, in the case of fire, prisoners are better off staying in their cells, as the cell doors function as firedoors?
Think of it like soccer riots, when you get a large group, they feel like they are invulnerable, but single one of them out and he’s a complete coward.
Individuals in a large group may well take a chance they would never do on their own, there is also bravado where one individual plays up to a crowd - take away the audience and their reason for challenge disappears.
Large groupings can also generate peer pressure among disorderly groups to join in, and of course sheer pressure includes threats to make the unwilling to join in the disorder.
Finally, there is the fellowship factor, or ‘us against them’ - enemies or non-associates will band together to challenge the authority figures.
Not to mention that once something does start, large crowds can add to the confusion, making it harder to put a lid on it before it gets worse.
The overwhelming majority of fires in prisons are cell fires, getting a figure of over 80%.
Being locked in your cell along with your nice warm friend is not a recipe for a long, happy or healthy life.
The main cause of those cell fires is deliberate - though occasionally electrical equipment is also responsible for a few - usually because prisoners have modified some items to improvise things such as cell phone chargers.
If there is a cell fire, the assumption is that it is deliberate, and that an irate prisoner is waiting behind the door with an improvised weapon to assault the cell rescue/extraction team. With this in mind we have our priorities and procedures and no more shall I say on this.
The other hot spot is in prison workshop/employment. Again you have maybe 30 or so prisoners in one area, but with the added problem that there may well be tools and equipment in circulation that you do not want getting smuggled out and on to the accommodation units. Again we have our procedures to deal with these events - but evacuation and preservation of life is the priority, but security and overall safety of the establishment are significant concerns.
I usually tell prisoners that if they want to set a fire in my workshop, I have a set of keys and I am guaranteed to get out alive - but in your case, as a prisoner you don’t have keys - set a fire and the guarantee is less robust - you might get out, or we might carry you out later on - if we find enough of you. They generally take the point.