Since nobody else gave an answer I will try.
Firstly Shimano 10 speed mtb rear mechs require different cable pull to all road any speed and mtb 9 speed or below. Similarly drop bar road and mtb front mechs require different cable pull for any speed*.
The confusing thing, is that while currently most flat bar road (SL-Rxxx) front shifters have mtb cable pull, some don't, as seen later.
But for slick shifts it is not just the correct cable pull matching the front mech requirement that is important, it is also desirable for the front mech cage shaped to match the chainset, and not just for the double / triple distinction, but also for the largest ring profile, and minimum tooth difference maintained between the large ring and next (to avoid clash), and seat tube angle matching design assumption (for the mech tail to be not too high to cut capacity, and not too far back to make up shifts difficult).
Because of the above, if I were you I would look at what chainset I want to run, then see whether the front mech suits, then work out which shifters match the front mech. Specs are available for all current
mtb and
road flat bar shifters.
Don't assume all SL-R front shifters require FD-Rxxx front mechs (which require mtb cable pull). The SL-R770-D-L e.g. is different to SL-R770, and require standard, road front mechs, so does the SL-R780.
Further you should check to see whether the matching rear shifter works with the rest of your system.
For example, the
SL-R780/SL-R783 10 speed front shifters are for double/triple road mechs and chainsets, so the matching rear shifter would not suit any 10 speed mtb mech, since all 10 speed mtb rear mechs are DynaSys. Similarly, no Shimano 10 speed mtb rear shifter will work with any Shimano road rear mech.
I don't think you will have clash issue between mtb shifters and road flat bar brake levers (except colour

).
* except one can cheat by running mtb front shifters on road mechs since, although not ideal, pulling too much cable can be made to work