It's not in exactly the format you want, but these data are available from this University of Minnesota page (see Table 1, which also includes the length of the border in miles and various US overseas territories.
You could also create your list from this page.
In case the above University of Minnesota link goes dead (it's an old link) here are the data in CSV format:
state1,state2,length
AL,FL,196.1
AL,GA,291.3
AL,MS,323.9
AL,TN,146.7
AR,LA,166.5
AR,MO,325.3
AR,MS,282.8
AR,OK,198.2
AR,TN,125.1
AR,TX,65
AZ,CA,198.4
AZ,CO,0
AZ,NM,391
AZ,NV,181.4
AZ,UT,275.8
CA,NV,608.2
CA,OR,216.3
CO,KS,207.7
CO,NE,173.2
CO,NM,333
CO,OK,52.9
CO,UT,276.1
CO,WY,260.2
CT,MA,86.5
CT,NY,82.3
CT,RI,40.3
DC,MD,24.6
DC,VA,1.9
DE,MD,122
DE,NJ,1.4
DE,PA,22.6
FL,GA,261.4
GA,NC,68.6
GA,SC,249.6
GA,TN,72.6
IA,MN,262.1
IA,MO,235
IA,NE,148.9
IA,SD,85.6
IA,WI,86.7
ID,MT,569.8
ID,NV,153
ID,OR,305.8
ID,UT,153.6
ID,WA,210.3
ID,WY,170.7
IL,IA,200.5
IL,IN,295.5
IL,KY,122.4
IL,MO,331.6
IL,WI,144.4
IN,KY,296
IN,MI,108.4
IN,OH,178.8
KS,MO,307.5
KS,NE,356.5
KS,OK,409.1
KY,MO,59.8
KY,OH,155.5
KY,TN,338.5
KY,VA,119
KY,WV,79.1
LA,MS,456.6
LA,TX,222.7
MA,NH,86.7
MA,NY,49.4
MA,RI,62.6
MA,VT,40.9
MD,PA,195.7
MD,VA,253.7
MD,WV,174
ME,NH,159.3
MI,OH,69.7
MI,WI,205.1
MN,ND,217.1
MN,SD,180.8
MN,WI,291.1
MO,NE,53.6
MO,OK,34.4
MO,TN,60.9
MS,TN,119.2
MT,ND,210.8
MT,SD,65.3
MT,WY,377.7
NC,SC,312.2
NC,TN,218.9
NC,VA,327.7
ND,SD,359
NE,SD,399.4
NE,WY,138
NH,VT,180
NJ,NY,103.4
NJ,PA,150.9
NM,OK,34.5
NM,TX,536.2
NM,UT,0
NV,OR,152.5
NV,UT,344.6
NY,PA,306.1
NY,VT,80.3
OH,PA,92.4
OH,WV,243.5
OK,TX,715.4
OR,WA,385.8
PA,WV,118.6
SD,WY,137.7
TN,VA,110.7
UT,WY,173.1
VA,WV,381.2