The choice of anyone or everyone has no bearing on whether OP's sentence is "complete". The issue there is simply whether "that" refers back to some fact previously mentioned...
Speaker A: "Pigs can't fly!" Speaker B: "Everyone knows that." ("that" refers back to A's statement).
Speaker A: "Everyone knows that pigs can't fly!" ("that" refers forward, or to implied "the fact that").
Regarding the actual choice of indefinite pronoun (anybody, anyone, anything, each, everybody, everyone, everything, few, many, nobody, none, one, several, some, somebody, someone, etc.) there's no special grammatical reason for the overwhelming preference...
"but everyone knows that..." (74700 instances in Google Books).
"but anyone knows that..." (430 instances)
To a large extent, it's just the established idiomatic usage. But the preference reverses with...
"everyone can do that" (9,690 instances)
"anyone can do that" (56,200 instances)
...which I attribute partly to the fact that everyone effectively means all people, collectively, whereas anyone means any one particular person chosen at random.
When the associated verb is can, the "deed" is a single action (not even actual, just potential), so it makes more sense to link it to one person (any one you care to pick). But if you know something, and others know the same thing, it's more emphatic to say that all people know it (all the time).
When you sign something with a flourish you make a kind of bold dramatic motion of the pen.
I think it's a metaphor to living the end of his life, and how he would like to deal with it, in style and displaying good character.
Best Answer
It means that it's of some interest.