An Officer and a Congressman.

The conflict lies in Article I, Section 8:
"The Congress shall have Power...
"To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two years;
"To provide and maintain a Navy;
"To make Rules for the Government of the land and naval Forces;
"To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
"To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the Unites States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress..."

Things don't work well when the guys writing the rules and signing the checks are officers subordinate to the senior officers who must abide by the discipline and rules -- and who want more money for their pet projects.

There may be no real conflict of interest, however there could be a perceived conflict of interest.

As a Senator, any statement he makes is Public. As a Commander, regardless of whether he is in uniform or not, those statements can be perceived to be acceptable. "If he can say that, why can't I?"

It's less about him serving as an officer & a Senator, more as him holding a Command & an Office at the same time. Both are positions of authority, and perception is very hard to separate.