In total, there are 386 Pokemon in the FireRed/LeafGreen's National Dex, with 165 of those Pokemon being unobtainable in both of those games.
With only access to one cartridge and no trading, you'll miss out on two of the three starter's evolutionary lines, either the Omanyte or Kabuto line, as well as two of the three legendary dogs. These add up to 10 Pokemon you'll be unable to get.
Without trading, you also won't have access to trade evolutions! The trade evolutions in FireRed/LeafGreen are Politoed, Alakazam, Machamp, Golem, Gengar, Kingdra, Scizor and Porygon2. These add up to a total of 8 Pokemon that you can't get without access to trade evolutions.
(P.S. Huntail/Gorebyss/Slowking are excluded from here, as their evolutionary lines are already counted as either being unobtainable or version exclusive)
And lastly, we have Pokemon that are version exclusive to LeafGreen. Those being the Sandshrew line, the Vulpix line, the Bellsprout line, the Slowpoke line, the Staryu line, the Magmar line, Pinsir, the Marill line, Misdreavus, Sneasel, the Remoraid line, and Mantine. These add up to 23 Pokemon in total.
With this all into account, there are 180 Pokemon you can catch in FireRed alone.
Sources:
Unobtainable Pokemon
Trade Evolutions
Version Exclusives
