Looks like 2 recent sales for this item, pretty sure this is the only one that moved: https://backpack.tf/item/554275661

First sale: purchased alongside a Flaming Lantern Greased Lightning for 145 keys pure (https://backpack.tf/profiles/76561198042023311#!/compare/1654214400/1654905600)

The trade was quite clearly a quickbuy for these two items, buy orders for the Fro and Greased Lightning were at 87 and ~56 keys, respectively, during the time of the sale (June 10th from what I've gathered).

Greased Lightning Buyers: https://gladiator.tf/time-machine?item=Flaming+Lantern+Greased+Lightning&at=2022-06-10T10%3A02%3A00.000Z

Fro Buyers: https://gladiator.tf/time-machine?item=Flaming+Lantern+Demoman%27s+Fro&at=2022-06-10T09%3A33%3A00.000Z

Second Sale: Fro was traded for an Aces High Ritzy Rick, 46 pure, and Double Spelled Pro KS Genuine Nostromo Napalmer (https://backpack.tf/profiles/76561198140316312#!/compare/1658016000/1658102400)

Aces Ritzy is in-date at 29 keys: https://backpack.tf/stats/Unusual/Ritzy%20Rick's%20Hair%20Fixative/Tradable/Craftable/59

Only recent sales I could find for double spelled Genuine Nostromo Napalmers was 45 keys for a non-pro ks one (https://backpack.tf/profiles/76561198331420429#!/compare/1655510400/1656115200) and this sale at ~75 keys: https://imgur.com/a/9cCJSpn (provided by the person who traded me the Napalmer, this was their purchase of it)

One double spelled pro-ks Genuine Napalmer is currently up for sale for 90 keys and buy orders on classifieds are at ~46 keys for them, as can be seen here: https://backpack.tf/classifieds?item=Nostromo%20Napalmer&quality=1&tradable=1&craftable=1&australium=-1&killstreak_tier=3

The Napalmer is tough to price, but even if we disregarded the ~75 key sale and 90 key listing and value it at 50 keys, just 4 keys above buyers, the total trade value would come out to 29 + 46 + 50 = 125, which would be the cap this trade could be valued at since my buyout for the Fro was 125 keys: https://gladiator.tf/time-machine?item=Flaming+Lantern+Demoman%27s+Fro&at=2022-07-18T00%3A38%3A00.000Z

All that being said, I'm going to exclude the first sale due to it being a quicksell and suggest a price of 125 keys for the Flaming Lantern Fro based off of the second sale :)