I can play a lot of songs on the piano when I see them for the first time as sheet music, including a lot of original jazz arrangements and classical pieces. My sight-reading is pretty good but I do have difficulty in phrases where scales must be played quickly.
What are some practical ways to train my improvisation skills using my sight-reading ability?
The question is quite broad, however here are some tips:
Familiarize yourself entirely with scales and arpeggios. As boring as it sounds, it is incredibly important to know your way around a piano. Don't just familiarize yourself with major scales, work with natural, harmonic, and melodic minor, and even the blues scales! It is also a good idea to work with scale modes as well as they come in handy when improvising a song. www.notreble.com/buzz/2011/10/26/a-practical-guide-to-modes-and-scales/
Here is a good site for learning about all the kinds of scales.
Listen to the kinds of music you want to improvise. If you want to improvise like Chopin, listen to more of his piano sonatas! If you like Dvorak, listen to his piano concerto! Listen to more blues piano pieces if you want to improvise blues. The point is, it really helps when improvising if you know what you want your improvisation to sound like. Same thing in sight reading!
Learn how to modulate keys. Really important. You don't always even need to change keys, but it really helps to know what chords sound good together and which ones are more dissonant so you can appropriately place them in your song.
Familiarize yourself with chords! Not knowing your basic chords will prevent you from creating an impressive improvisation and it helps loads to know some more uncommon ones. www.pianochord.com/list-of-chords
Form a motif. This is the more creative part of improvising that will develop more over time. A motif, if you don't know, is a "brief melodic or rhythmic formula out of which longer passages are developed." Basically it is a theme. They are pretty short and the point of the motif is that you work around it and develop it. You probably won't immediately be amazing at this and that is why it is a skill that develops over time.
Familiarize yourself with the basics of music theory in general. Having a basic understanding of music theory such as time signatures, chord structure, melodic development, etc. will drastically improve your ability to do the techniques listed above.
Practice, practice, practice. This is pretty general, but practice your improvising. It is the only way to actually make physical bounds. It will take time, but with patience and practice, you will become greater and greater at it.
Comment if you have any questions about this answer! Good luck!
Apologies for not having all of the websites as hyperlinks. I only have permissions to make one at a time currently.