score:7
(Since I was requested to do this in a comment, and no closure or other answer appears to be forthcoming...)
My assumption on reading that passage, prior to even reading the text of your question was that in (Montaigne's?) phrase "that which Flaminius brought into their country", the "that" is referring to the "this army" from the previous quoted sentence.
A similar question about "that which" was raised over on the ELU site. Its a somewhat archaic turn of phrase. The accepted answer there contained this:
The that is a pronoun referring back to a noun phrase and the which is the relative pronoun used for non-animate antecedents
The King James Version of the Bible is about the only place a modern English reader is liable to come across this turn of phrase.
Upvote:5
This is just a confirmation of T.E.D. answer, but too long for a comment.
Michel de Montaigne wrote in French (when not in Latin), and the original text is available online:
Quand le Roy Pyrrhus passa en Italie, apres qu’il eut reconneu l’ordonnance de l’armée que les Romains luy envoyoient au devant, je ne sçay, dit-il, quels barbares sont ceux-ci (car les Grecs appelloyent ainsi toutes les nations estrangieres), mais la disposition de cette armée que je voy, n’est aucunement barbare. Autant en dirent les Grecs de celle que Flaminius fit passer en leur païs, et Philippus, voyant d’un tertre l’ordre et distribution du camp Romain en son royaume, sous Publius Sulpicius Galba.
(emphasis mine)
In French there is no ambiguity: the construction "de celle que" (translated as "that which") clearly refers to "l'armée" ("the army"). In short, Greeks were impressed by the organization of Flaminius' army and Philippus by Galba's as well as Pyrrhus had been impressed by the army Romans had sent towards him.