The Cambion has a spear attack (MM p. 36):
Spear. Melee or Ranged Weapon Attack: +7 to hit, reach 5 ft. or range 20/60 ft., one target. Hit: 7 (1d6 + 4) piercing damage, or 8 (1d8 + 4) piercing damage if used with two hands to make a melee attack, plus 3 (1d6) fire damage.
Is the +1d6 fire damage a property of the spear, or the Cambion?
The cambion's spear attack does fire damage, but no rule says that the spear itself retains that property.
A statblock only defines what a creature's attacks do, not the game statistics of any items they may carry. In this case, the cambion may make a spear attack dealing 1d6+4 damage plus 1d6 fire damage, but there is no rule or descriptive text which would define that the spear retains that property.
The ethos of D&D 5th edition is that a rule says what it says and no more.1 Therefore, the rules say only that the cambion deals extra fire damage with his spear attack, not that the spear itself deals that damage in anyone else's hands.
It's also not common (perhaps unprecedented)2 for a creatures in D&D 5th edition to have a specific magic item in their statblock. Treasure from encounters is handled under its own rules in the Dungeon Master's Guide.
Lore-wise, the cambion has many supernatural abilities, specifically including the ability to create and throw fire, so it's very easy to imagine that fire surrounds any weapon he wields; conversely, flaming weapons are quite rare and difficult to acquire3, so many would not have this specific item.
Of course, the DM's word is law, so you could as DM say that cambions do indeed carry actual magic flaming spears, but only if you want your player characters running around with a load of flaming spears after they defeat an army of cambions. For that reason, I don't recommend it.
1 This is a design principle put forward by D&D 5e core designer Jeremy Crawford, and is widely used as a guideline for DMs adjudicating ambiguous rules. For example, in How much fire damage does igniting Grease deal?, Crawford's interpretation is that Grease isn't flammable because the rules do not say that it is. This attitude contrasts with D&D 3.5 where the DM was specifically advised to interpret ambigious rules by inference from other similar rules.
2 The only instance I'm aware of where a monster is described as having a magic item is the flind in Volo's Guide to Monsters, whose descriptive text says "It wields a flail imbued with powerful magic by Yeenoghu himself". However, even in this case, the statblock does not describe the weapon itself, only the attacks which the flind can make. It does not specify what happens if a PC tries to wield the flail, nor even is it made explicit whether the flail is a magic item, or merely temporarily imbued as a warlock may imbue his pact blade. If a DM ruled that a PC gains all the flail attacks the flind had, that PC now has a weapon dealing 4d10 bonus psychic damage, which is exceptionally powerful for an item you might gain around level 9, and I do not believe this was the designer's intent.
3 According to the item guidelines, magic items are only found in hoards, rather than standard per-monster treasure. The guidelines suggest that the PCs will in total acquire around 18 rolls on the CR 5–10 table, or 3 hoards per level, and 80% of these hoards will not even reach level Table F, the first table to give a +1 weapon. A cambion could have a magic weapon, but most won't.
Spear. Melee or Ranged Weapon Attack: +7 to hit, reach 5 ft. or range 20/60 ft., one target. Hit: 7 (1d6 + 4) piercing damage, or 8 (1d8 + 4) piercing damage if used with two hands to make a melee attack, plus 3 (1d6) fire damage.
Some monsters do have statements that explicitly call out the source of the extra damage such as the erinyes:
Hellish Weapons. The erinyes's weapon attacks are magical and deal an extra 13 (3d8) poison damage on a hit (included in the attacks).
and the weapon statblock is worded similarly to the one for the cambion:
Longsword. Melee Weapon Attack: +8 to hit, reach 5 ft., one target. Hit: 8 (1d8 + 4) slashing damage, or 9 (1d10 + 4) slashing damage if used with two hands, plus 13 (3d8) poison damage.
We do not get such an explicit clarification for the cambion so it will come down to a DM's decision.
However, even without an explicit statement anywhere in the statblock, it seems very logical and reasonable to assume that this extra damage is related to the fiendish nature of the cambion and not a special property of the weapon. It is clear from the wording that the damage is bonus damage that is separate from the weapon itself. Seeing how most of the cambion's abilities are fire-related added it makes a lot of sense to attribute the bonus damage to that and not to some unspecified special quality of the weapon.
The base damage die of the spear attack is consistent with the damage that a normal spear does: 1d6 one-handed and 1d8 two-handed. The attack is simply called "spear" and does not give any indication that the weapon is somehow different from any other spear.
In the end, it is up to the DM to decide what weapons an enemy has and what their properties are.
(Probably.)
It's not clarified in the stat-block, and the Cambion description is woefully scarce. Consequently, I went back to earlier editions of the Cambion (4th - Monster Manual I, 3.5 - Demonweb Pits Web Enhancement, and even 2nd - Planescape Monstrous Appendix).
In 4th, two Cambions are detailed, one of which has a flaming weapon ability; in this case, the equipment block reads simply "greatsword," meaning the flaming ability is innate to that Cambion. (An unofficial player writeup provides it as a racial feat.) This is the most recent prior version of the monster, but 4th and 5th are more different than similar, so I wanted to substantiate it from prior material.
In 3.5, cambions have an innate "aligned strike," which causes weapons they wield to become evil- and chaotic- aligned, but it only helps them overcome damage reduction. However, they're considered to be CR 5 (and are suggested to advance with levels in Assassin or Wizard) and their descriptive text indicates that they prefer poisoned or magical weapons (which they can qualify for as loot, given their base CR).
Finally, in 2nd, the cambion has no innate abilities that enhance their weapon, but does have this text:
Many have a magical weapon (75% chance), most likely of common make (i.e. +1, +2, etc.), but 15% likely to be special (referee's choice).
Given all that, and the fact that the 5th ed cambion isn't described as having any innate "flaming" ability (which seems relevant if the DM wishes to vary them as enemies)... it seems very likely that the 5th ed Cambion is a callback to earlier days of the monster, and comes equipped with a flaming spear by default (befitting their role as soldiers in the armies of the Lower Planes). Since the weapon is innately magical, then players would also benefit from its magic if they loot it.
