Trying (and maybe failing) to think this one through. Possibilities as I see them:
1: Trump wrote the Tweet and Dowd is taking the blame.
2: Dowd wrote the Tweet without Trump's input or approval.
3: Dowd wrote the Tweet with Trump's approval.
Testifying to options 1 or 3 would, I think, be adverse to Trump's interests and require disqualification.
Option 2 is more complex. On it's face, it's not clearly adverse to Trump.1
But then we get to the follow-up questions, which will involve Dowd's knowledge when he wrote the statement. Dowd was hired, IIRC, in June, so he won't have firsthand knowledge. His information will have been acquired through conversations with his client that would ordinarily fall within the scope of attorney-client privilege. But does the privilege survive the Tweet? I have no idea, but I do know that Mueller hasn't been shy about attacking the privilege.
If the privilege survives, Dowd probably doesn't have to withdraw. If it doesn't, that brings us to the follow-up options:
4: Dowd knew Trump knew, believed, or strongly suspected that Flynn lied to the FBI when he fired Flynn.
5: Dowd knew Trump did not know Flynn lied to the FBI when he fired Flynn.
6: Dowd didn't have any idea what Trump knew when he freelanced.
Testifying to 4 would be adverse to Trump's interests.
Testifying to 5 or 6 would not necessarily be adverse to Trump's interests, and would instead merely involve Dowd testifying that Dowd had made a truly stupifying blunder that calls his fundamental competence as an advocate for his client into question.
1: But it might be adverse to Dowd's own personal interests.
I believe that each era finds a improvement in law each year brings something new for the benefit of mankind.
--Clarence Earl Gideon