I transcribed Miles solo on this tune. I think its a cool tune, an interesting variation of the minor blues.

One of the biggest challenges I've found in jazz guitar playing is getting a more legato type of sound. Its especially hard when playing along with the trumpet, an incredibly legato sounding instrument. I think sometimes when I play, I have too much a stacatto, "plunking" kind of sound, if that makes any sense. So any advice from other jazz players on how to alleviate this problem would be appreciated.

Here's the recording.
I couldn't think of a thing that I hope tomorrow brings
Slurs are really effective with chromaticism, this is what is generally accepted with bebop. look at it from the point of tension and release. just from that brief line you should aim to hit the first note, the Bflat as staccato and then hit the B natural and while doing so hammer onto the C before falling on the G to release the phrase.

The first note is the tension and attack while the next two notes are travelling towards being resolved.

And you don't have to use legato all the time, its something you have in your head that can be pulled out at any time.

Your video reminds me that I really need to transcribe, I haven't done it in ages haha. Great work on the transcription by the way.
A number of things can contribute to a smoother, less stacatto sound. The first is your gear. I'm told that nylon picks get a softer pick attack, which would give you a smoother, less abrupt pick sound. Make sure you're using your neck pickup. Try to roll back the tone somewhat and check your EQ to be sure that you have a strong mid presence.

Now, technically speaking, you could do hammer-ons and pull-offs on chromatics instead of picking each note. That is certainly an option, but I would recommend you go even further. Pull-offs can give a fairly sharp, almost stacatto sound, which can really mess up a smooth sounding run. To avoid this problem, try to use reverse hammer-ons. Alan Holdsworth used this technique extensively (there are lessons here and there on the web that explain better than I can; don't watch Marshall Harison's videos (he's a poor teacher at best)). If you're familiar with this technique, give it a shot. If you aren't, take a look and see if you can't try to get the gist of it. It's a useful skill.