Tolkien's apparent final word on the number of Balrogs is given in commentary to paragraph 50 of section two of the Annals of Aman, published in History of Middle-earth 10: Morgoth's Ring:
There should not be supposed more than say 3 or at most 7 ever existed.
Going by the lower limit, the three Balrogs are therefore:
- Gothmog, Lord of the Balrogs (slain by Ecthelion)
- The unnamed Balrog slain by Glorfindel
- Durin's Bane, the Balrog of Moria
If we accept this lower limit, and noting that the text states "there issued from Angband Balrogs to aid them", so therefore "Balrogs" implies more than one, we can say the following:
- It took either two or three Balrogs to defeat Feanor
- Feanor killed none (because all three are otherwise accounted for)
The published Silmarillion favours a number of Balrogs towards the higher-end of the "three-to-seven" range, because the last chapter (Of the Voyage of Earendil and the War of Wrath) notes that:
The Balrogs were destroyed, save some few that fled and hid themselves in caverns inaccessible at the roots of the earth...
So in addition to the three above we have:
- More than one (again because "Balrogs" is plural) that was destroyed.
- At least one more ("few" being plural, and in addition to Durin's Bane) that escaped.
That makes it at least three more Balrogs, so the minimum number therefore becomes six. If there were seven but we now have six accounted for, we may surmise that the seventh was killed by Feanor, but there's absolutely no textual evidence to support that assumption: there may have been only six, or the seventh may have been an extra one in either of the above two categories. (Yes, that means that there is at least one and possibly even two Balrogs still loose somewhere in Middle-earth at the end of the Third Age.)
Putting it all together, we therefore get the following combinations of possibilities:
Accounted for 3 3 3 3 (Gothmog/Glorfindel's/Durin's Bane)
Killed by Feanor 0 1 0 0
Killed in War of Wrath 2 2 3 2
Also Escaped 1 1 1 2 (In addition to Durin's Bane)
Total 6 7 7 7
If it suits your own perception of Tolkien's stories to have Feanor as a Balrog-slayer then you can certainly have that: Tolkien doesn't say that he did, but then again he doesn't say that he didn't, so you can have it either way. Nor is there any indication of how many of those were involved in killing Feanor.
It's notable that the above quotation dates back to the 1937 Silmarillion and was published completely unchanged. At that time Tolkien did still imagine a far greater number of Balrogs than he subsequently came to. That's also interesting because it shows that Tolkien had imagined Balrogs surviving "in caverns inaccessible at the roots of the earth" well before he came to concieve of the Balrog of Moria.