Yes indeed Robert Daniell had a coat of arms, no doubt issued by the College of Arms, London (as would have been the case with British nobility who were not principally Scottish, the Scots having the Lyon Court to handle armorial matters). The important thing, though, is that the arms are only owned by one person. Today those arms are the heraldic property of the most direct descendant of Governor Daniell. However, others in the family can use a differenced version of the arms to show relation as long as the "mark of cadency" is sufficient to show that they are not the same arms. The crest could legitimately (in the US) be adopted by anyone...remember that the crest is the device that sits on top of the helmet, and the helmet sits on top of the shield. The shield itself is the "arms," and the whole thing together would be the full achievement of arms. There are only so many items that can be used as crests, which is why one sees the same basic crest on different peoples' arms. However, one might still consider making one's personal crest a slightly different vesion of Robert Daniell's crest.
These arms are listed in the Daniell Family History by Clara Williams. The blazon, or heraldic description, for the most basic arms I see in the book (which have ended up being quartered with other arms as other arms were acquired over the years) is as follows: Argent a pale furilly Sable.Upon the shield is placed an esquire's helm. Issuant from a torse of the liveriesis set for a crest a tiger statant regardant Sable with tail expanded, and charged with a fleur-de-lis Or for difference. Below the shield upon an escroll is this motto, "Pro Fied et Patria." This basically means the shield is white with a black jagged diamond pattern that sort of looks like an Argyll sock pattern. The crest is a black tiger standing and looking over its shoulder, and it has a gold fleur-de-lis drawn on it. The torse is a wreath on which the tiger stands, and is in the liveries, i.e., white and black.
Not having a color rendering, I can't give you the full blazon for the multiple-quartered arms shown on the front of the Daniell Family History book.