Button and bullet ID needed

[2moshers]

Found this button and bullet in two adjoining farm fields. The very small button has a flag/banner with an anchor across. I'm thinking the bullet, which is solid, is somewhat old but am not sure. Thanks for any help.

 

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[relic nut]

I know nothing about the button. The bullet does look old due to the oxidation. It has vertical lines in the groove which I think are called cannelures . someone correct me if I am wrong. I was told that they didn't start using these until after CW. Late 1800 .