Cliffs:

SB's check/jam range:
AA,TT,22,ATs+,A2s,KhQh,KhJh,QhJh,KhTh,QhTh,JhTh,AT o+

MP's flat flop range:
AA,TT,22,ATs+,A2s,KhQh,KhJh,QhJh,KhTh,QhTh,JhTh,9h 8h,8h7h,7h6h,6h5h,5h4h,4h3h,3h2h,AJo+, 45 combos

MP's call a flop shove range:
AA,TT,22,AKs,ATs,A2s,KhQh,KhJh,QhJh,AKo, 19 combos

Our fold equity against MP if we shove: 26/45 = 58%

Our equity against SB alone: 50%

Our equity against MP alone: 29%

Our equity against both together: 14%

Pot size after SB shoves: $25.25 and $6.85 to us to call

Three-way main pot size if we shove and MP calls: $38.95 incl our bet of $6.85

Side pot size if we shove and MP calls: $35.30 incl our bet of $17.65

Just to give us some idea of where we're at in this hand, the EV of a flop shove is:

EV(we shove and MP folds) = .5 * 25.25 - .5 * 6.85 = $9.20

Main Pot EV(we shove and MP calls) = .14 * 32.10 - .86 * 6.85 = -$1.35

Side Pot EV(we shove and MP calls) = .29 * 17.65 - .71 * 17.65 = -$7.41

Total EV of shove (with these approximate ranges):

.58 * 9.20 - .42 * (1.35 + 7.41) = 5.34 - 3.68 = $1.66

Well not that much after all, and folding is certainly reasonable given the huge variance. But it does look to be +EV and if you're rolled for it and want to play a potentially epic hand, I say go for it.