Let's talk about the best Fire-type attacker

There isn't much between them, but I will let others list of their virtues in detail.

One question though...you talk of their ability to last in a fight, using only stamina as a factor, but have chosen to remove defence from the equation. Why?

The ability to last in a fight is determined by both stamina and defence, and is usually listed as 'bulk' (a combo of both stamina and defence).
Is there a particular reason you wish to remove defence from the discussion?

One major difference I will point out is that Moltres has flying typing to consider, which gives it an edge in many of the meta relevant match ups that you would use a fire type for.

I would suggest that one reason that Flareon is considered a better choice is the availability of Flareon and candy to power up...most people would already have at least one Flareon if not an army - legendaries are not as readily available to all players equally.

I'm not sure where you see people saying Flareon is the best, except in comments that are months old. Moltres has been the strongest fire-type attacker since summer. It is indeed a no-brainer and I think most people are aware of it.

Entei vs. Flareon is more interesting. Despite the lower attack, Entei actually outperforms Flareon in simulations about 50% of the time. This could partly be due to its lower defense that lets it generate energy faster, and it can also be in part because its higher overall bulk lets it more reliably get off multiple Overheats, where Flareon is a lot more fragile. Depending on matchup, Flareon will generate a bit better DPS, but the difference is small enough that usually you should pick Entei over it anyway.

Regarding the difference between Moltres and Entei then, Moltres gets even better in most relevant matchups due to its secondary typing. It double resists grass and bug and also potential Earthquake from Metagross (speculation, but could be a thing). Entei however is a better pick against ice-types.

EDIT: The upside of Flareon is that you can get it at L30 without stardust. It has the best ratio of usefulness to resource cost.

When were you doing your research? Whatever comments you were looking at must have been before raids.

Moltres is the highest DPS fire pokemon.

Flareon is really close behind it in DPS, but is more fragile. It is still a good choice if you don't have a legendary fire attacker.

Entei has lower DPS, but is much tankier (def*HP) so it will last longer. Its huge HP reserve will also allow it to gain more energy.

I don't think here Flareon has been "consistently mentioned as the best fire type".

Moltres offers the highest fire type DPS in game, and because of its flying type it has resistances against a lot of the things fire counters. If it's all about doing more damage in a given time and especially if tight on time in Raids, Moltres is a beast.

Entei has less attack but is bulkier, and has access to Flamethrower which is better suited for gym battles (overheat is usually overpowered for regular gym battles).

Also, tankiness is DEF x Stamina so when you talk about how long some attackers can last in battles, both stats should be mentioned.

In reply to your answer you will see Flareon mentioned more simply because it's the easiest to power up...legendary candies are harder to come by so it makes sense to power up Flareon and make moltres or entei your project.

For myself I would grade them as follows mainly because I use them for raiding.
1) Entei
2) Moltres
3) Flareon

It's better to have a tanky pokemon like Entei which is also able to fire off a few overheats before it faints unlike the much more glassier Flareon.