I disagree with IT Tsoi's answer. Triethylamine absolutely will compete, and form ammonium salts. Those salts may react with 4-phenylbutan-2-amine to lead to product, but more likely they will precipitate. And be general gunk in the reaction flask. Pyridine will probably be less of an issue.
In general direct alkylation of amines is a pretty ugly reaction with overalkylation products likely. A better reaction in this vein would be to make the acetamide and alkylate that with the chloroacetophenone, and then deacetylate, or similar strategy.
If you must alyklate the amine, use Hunig's base (N,N-diisopropylethylamine) which is too sterically hindered to alyklate. Also, add the electrophile to excess nucleophile, if the reaction is faster this will decrease polylaklyation probabilistically, and the carbonyl alpha to the amine may have enough electron withdrawing character to slow down the increase in nucleophiliciity that you get from a more substituted amine.
Further mucking up this route is the phenol with two carbonyls on the ring, that is probably quite acidic as well, and may be deprotonated with the base scavengers. Use a phosgene protecting group to cover up both the phenol and the aramide, and this problem will be side-stepped.