Difference between 他带来了很多衣服 and 他带很多衣服来
Essentially, your question concerns the positioning of the auxiliary verb 來[来] in a sentence. There are two meanings of 來:

To indicate an observed movement caused by the main verb (帶[带]) towards the speaker

To indicate the start (or in a more abstract sense, consequence) of the action caused by the main verb


It is good practice to place it immediately next to the main verb of the sentence, especially if it only consists of one character. You may also treat 帶來 as a compound verb.
I am in no position to say that the second sentence is ungrammatical, perhaps just a bit too colloquial. Because there are indeed situations where the 來 can be placed after the object (i.e. 很多衣服 in your sentence). In fact, your second sentence even sounds perfectly fine to my Cantonese ear. Here are three grammatical examples in written Chinese where the 來 is placed after the object:

The famous nursery rhyme 掀起了你的蓋頭來 [掀起了你的盖头来] (lift your veil [lit. head cover])
A primary school text titled 讀出許多東西來 [读出许多东西来] (inferring [lit. read out] a lot of things)
Or this biblical excerpt: 「就像一個家主從他庫裡拿出新舊的東西來。」 [就像一个家主从他库里拿出新旧的东西来] (“Like a master of a house, who brings out of his treasure what is new and what is old.” Matthew 13:52)

Note that the main verb of these three examples are already compound in nature: 掀起 (lift up), 讀[读]出 (read out/infer), and 拿出 (bring out). It may then be permissible to put the auxiliary verb 來 after the object, perhaps for the sake of readability.