It's actually 並列構詞. 瞻 and 仰 have similar meanings.
The earliest record of 瞻仰(瞻卬):
詩 大雅 雲漢:“瞻卬昊天,有嘒其星。” (西周初年至春秋中葉)
At that time, 瞻 and 卬 were treated as separate words. Their meanings are similar.
瞻:向前望或向上望 as in 詩 邶風 燕燕:“~望弗及,泣涕如雨。” It's extended to mean 敬仰,仰望, as in 詩 小雅 小弁:“靡~匪父。” (to look forward or upwards > to venerate)
卬: 舉首向上 as in 莊子天地:“爲圃者卬而視之,曰:‘奈何?’” or 望 as in 國語晉四:“重耳之卬君也,若黍苗之卬陰雨也。” It's extended to mean 敬慕,信任, as in 荀子 議兵:“上足卬則下可用也,上不足卬則下不可用也。” (to raise your head/loop up > to look into the distance, to venerate and trust)
As a 並列詞組, technically at least in early periods either order was possible. But in this case I cannot find a single case. It's probably because 瞻 has an ending m sound in Old Chinese and thus requires a closing mouth. 卬 doesn't. It's easier to end a phrase with an open-mouth sound. Or it is simply because the 詩 quote is so famous that people use it idiomatically. Or it's possible that the other word was used before 春秋 and written records were lost. Or it's simply that I didn't search through.