The plant is as seen below, in the photographs, and is similar to cyclamen / sow bread in all respects, but I am absolutely certain that the flower belongs to neither, and the only other plant that comes to mind is a buckflower. Am I right?
It is one of the Heuchera/Heucherella varieties, of which there are many, probably hundreds. Heucherella is a cross between Heuchera and Tiarella - Tiarella tends to produce longer flower stems. As to which exact variety you have, given the range of plants in this category, it's hard to be precise, but it might be something like Heuchera 'Paris' - information and some images here https://www.plantdelights.com/blogs/articles/coral-bells-heuchera-plant-varieties
The flowers on these varieties are usually fairly insignificant - they are grown for their decorative leaves more than anything else, and their ability to tolerate a fair bit of shade. So far, the only Heuchera which produces noticeable and attractive, bright red flowers is Heuchera sanguinum, like the variety 'Firefly'; this is one of the original Heucheras prior to breeding and crossing, and it has plain green leaves. The common name 'coral bells' refers to the bright red flowers on the original plant.
It looks like it wants to belong to the Saxifrages, a rosette of palm shaped leaves with a long spike/raceme of flowers. However this one is on steroids, perhaps sitting in the garden of a scientist who brought one from a remote region and gave it a favourable environment.
If by buckflower you mean Eriogonum thymoides, these have flowers in a head, but the picture shows a raceme, a spike with flowers on short stalks so maybe the answer to your specific question would be no.