Hmm, not entirely sure since the game was never meant to be ran via Dosbox emulator so you can try to just change the cpu type from Auto to pentium_slow which might also help. I tried it on mine and it seems a little better at least. It's either that or go to the thread with the Windows port and give that a shot. The only problem is that windows port wasn't meant to be used with the gog.com version so the music won't play. :(
That's not exactly true since GOG version is standard version, not the Plus one, and Freesynd port only didn't support Syndicate Plus edition which is basically Syndicate with integrated American Revolt and other hardcoded resource/executable edits.
Not working Panic mode (right and left mouse click do nothing.
Missing Tension music (when your agents are attacked).
Probably still not working radar.
Good thing is you can have 4 female agents by default, this wasn't possible in original game, neither have more than initial 3 or acquire new ones, male stuff only but not that difference in-game.
Either on native DOS 6.22 or DOSBox - mind you the game has very limited rendering engine in terms of drawing sprites and action on screen, it doesn't crash but can be simply exceeded to massive slowdown, so when you have 40-60 persuaded followers and many explosions it will lag, obviously. You can set more memory in memsize but that will not necessary solve problem in old days DOS based games and DOS itself has limited memory and CPU capacity so the games that use them.