Hopefully I have understood the rule of first mention correctly, but I do not think there is warrant for it as an absolute law for a couple of reasons.
First, in terms of allegory in the Scriptures, one thing can often be a stand in or symbol for multiple other things. Moses, for instance, is a type for Joshua (Joshua 3:7). Moses parted the Red Sea, and Joshua parted the Jordan. Moses gives the covenant, and Joshua renews the covenant. Yet Moses is also a type for Christ. Moses gives the law from the mountain, and Jesus delivers a greater law in the sermon on the mount. Moses delivers the people in the exodus and Jesus too leads the people in a new exodus (Luke 9:31). If we were to follow this rule as a law, we would have to conclude that Moses was only a type for Joshua.*
Or again, the serpent in Genesis 3:1 represents Satan (Revelation 20:2). Yet, if we hold rigidly to the rule and allow only Genesis 3:1, being the first mention, to set the symbolism of serpents, then we will fail to see how the serpent that is lifted up in the desert by Moses is a symbol of Christ (John 3:14).
Second, especially in apocalyptic literature, the author often times explains the symbols, even if similar symbols have been used before in Scripture. For instance, a similar use of clothing to your example can be seen in Zechariah 3 where an angel takes the high priest's clothes which are smeared in excrement and changes them for new fine clothes. And in doing so he explains the symbol: "See, I have taken away your sin." Similarly in Revelation 19:8, John explains, "Fine linen stands for the righteous acts of the saints." If John instead had written, "Fine linen stands for new resurrection bodies", we wouldn't say, "Nice try, John; but we already know because of the rule of first mention that fine linen cannot stand for resurrection bodies." The fact that the authors can and do explain their own symbols suggests that they are not constrained by the previous use of an object as a symbol.
That said, the rule is not all bad. Earlier texts quite clearly set the trajectory of our interpretation of later texts. Every text is written in a context, and the earlier writings naturally provide context for later ones; otherwise we can't make sense of allusions or even quotations which are so obviously present in the later texts. I don't know that I have a Biblical argument for this, except that the later writers were clearly influenced by the earlier ones and it makes sense that they would be influenced in their choice of symbols by the Scriptures before them, even as they had freedom to pen new metaphors.
* Someone might object that Moses and Joshua simply look like one another because they are both types from Christ. There are at least two reasons I would dispute this. First, the Bible itself makes the connections between Moses and Joshua explicit. "The Lord your God did to the Jordan just what he had done to the Red Sea when he dried it up before us until we had crossed over" (Joshua 4:23, cf. Psalm 114). Second, Moses is a type for Joshua in ways that he is not a type for Christ. Moses removes his sandals (Exodus 3:5) and Joshua removes his (Joshua 5:15). Jesus does not remove his sandals; instead he comes as one whose sandals John is unworthy to untie. In fact, I would argue that part of the typology of Joshua is that he is a New Moses who anticipates a greater New Moses still.