He likely would if he could, unfortunately (for him) only a party to the case "defense or prosecution" can file an appeal, and because both parties want the case dropped neither are going to appeal. The Judge can't "appeal" as he is (supposedly) a neutral party so doesn't have the standing to appeal anything.
Now Judge Sullivan did try to "backdoor" an appeal by appointing a fellow left wing judge as a supposedly "unbiased" 3rd party (who of course issued a finding saying that the Flynn case should continue). But that went nowhere at the appeals court because they rightfully said a 3rd party brought into the case by a Judge as no more right to appeal than the Judge himself.
What hes doing is hes hoping his hand picked stooge will ask the full court to review it. At a minimum that would delay the decision until after the election, which is probably his real goal. He probably doesnt feel comfortable telling the guy to ask for a full review. So hes reduced to dragging his feet in the hope that he takes the hint.