Pretty sure Henry is unable to die as long as he can passively retry to an earlier point
As for the match, this seems pretty tricky since both of them are capable of loading to earlier points which would sabotage each other. However, it should be noted that after a while, Flowey ended up losing control of the SOULs inside of him due to Frisk saving them. Henry would be able to look up a walkthrough of the battle to realize Flowey’s weakness, and even if Flowey loads, Henry has Acausality from remembering his previous fails where some even led to his death.
Alternatively, he could try to completely alter Flowey’s appearance and personality by using Convert through chanting a short phrase which would make Flowey his own ally forcing him to work for Henry, to a point he may not be able to load due to working for him..