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My information differs from yours. Frederick, b.1774 married (1) Rachel McElfresh, license Dec. 1, 1801, had 3 children: Philip, b @1802, Lydia, b.1804 and Eleanor, b.1806. He then married Elizabeth (Betsy) McElfresh, license Oct. 6, 1809 and they had six children: John Hamilton Smith Linthicum, b.1812, Frederick, b.1826, Otho, b.1833, Thomas, Ann & Elizabeth.
Your Frederick, b.1774 is a brother to my Hezekiah, b.1773....their parents were Zachariah and Sarah (Prather). Does any of this help?