There are similarities and differences. Fingerings of the oboe and saxophone are similar to the flute (but not identical).
The basic fingerings (D, E, F, G, A, B) are essentially the same in the lowest octave (if the flute LH thumb key is closed). Flute, oboe, and saxophone are all octave based instruments. The second octave fingerings are mostly the same as the lowest octave. The big difference from the flute however, is that the oboe and sax use an octave key to jump to the second octave, whereas on the flute the second octave is achieved by overblowing to the next harmonic. In the third octave, the fingerings are different on all three instruments.
The clarinet is not octave based. Instead it overblows a twelfth. The lowest octave is called the chalumeau register and the fingerings are offset by a twelfth from the flute fingerings. For example, on the flute, oboe, and sax, with the first two fingers of the left hand down, they all play a written A. On the clarinet in the lowest octave, the first two left fingers play a written D below the staff. With the same fingering, but adding the register key, the clarinet jumps up a twelfth to the A one ledger line above the staff.
The flute has little resistance when blowing. Flutists are always trying to conserve air to keep from running out. The oboe has great resistance, so it's exactly the opposite of the flute. Oboists sometimes have to exhale excess air before taking another breath. In terms of resistance, the order (from least to greatest) would be flute, saxophone, clarinet, and then oboe.
So, for a flutist, from the perspective of fingerings only, it would probably be initially easier to learn oboe or sax. IMO, the saxophone would be the easier instrument for a flutist to learn. The fingerings are closer in the first two octaves and the embouchure is looser on the sax than on the clarinet or oboe so there's less likelyhood of interfering with your flute embouchure.
"Never give a flute player a screwdriver."