When we first meet Francis near Strawberry, he seems to be very enthusiastic about the rock carvings, stating that those carvings are "sort of important" to him. He also mentions that he's lost and that it's a long story. My theory is that he had only time traveled once and by accident.

Collecting:

Francis Sinclair's card says that his occupation is collecting, in his case, he collects rock carvings and their information about the past. Since he appears to be obsessed with history, he probably travelled to the 1890s after discovering 2 of the mural's carvings. A newspaper article about Francis' work mentions that he's a local resident in Strawberry, this means that he has been living there for months or even a year using a fake name (Frank Sinclair).

Epsilon Program?:

No, he's not Kraff, the first argument of my theory already disproves that speculation. But he's probably one of the founders of that religion in the HD universe of Redemption. Dan Houser stated that the Epsilon Program can exist in different places and times, using this information we can say that this could be the case. The rock carvings he tries to find were probably made by ancient people like him. Kraff descendants? It's a high possibility because those beings left messages in the shape of rock carvings. To end this argument, Francis Sinclair's mural indicates that he has convinced himself of being a demigod, and intends to solve this mystery by going to different times or universes (we don't know if time travel is the only limitation to his powers) in search of more information about his own race of "special humans".