This is what I came back with when I went and tidied it up, I could go ahead and make the rdr a variable if you would still like, but because it is only one rdr and not a few of them, I don't think you need to declare a variable to state it the one time
(unless you plan to expand this formula to include other functionalities).
Let me know, happy to help! It was just missing some quotations,
"<a class='Vibrant Danger' href='" & Dbid() & "?a=API_EditRecord&rid=" & [Patient ID#] &
"&apptoken=b3ya2etdy9kh2hdshehaabdzyq6e&_fid_252=" & "Failed - Kick Back to CC" &
"&_fid_243=" & "Level 0 - Call Center" &
"&_fid_247=" & "Missing Patient Information" &
"&rdr=" &
URLEncode(URLRoot() & "db/" & Dbid() & "?a=dr&rid=" & [Patient ID#]) & "'>Kick Back Missing Patient Info</a>