Can I use existing dictionaries (American Heritage, Merriam Webster) to compile my own derivative dictionary?

The below does not constitute legal advice, does not form an attorney-client relationship, and should not be relied upon to take or refrain from taking any action.

The copyright that attaches to dictionaries is quite thin --- but it nonetheless exists and protects the publisher's selection of words, the particular way the definitions of those words are phrased, and the supplemental information provided such as the words' etymology, slang applications, and usage examples.

I think you would be teetering on the edge of infringement -- if not falling over -- if you take 2 dictionaries, copy their word lists, and paraphrase their definitions into a consolidated "new" dictionary. The publishers of those dictionaries would likely object.

If the raw material for your dictionary was 50 dictionaries, however, and you exercised creativity in selecting the particular words and crafting your version of the words' definitions and added your own supplemental information then the publishers of those dictionaries would have no complaint.