Would an existing 2x10 front mech work with a new 11 speed rear set up? Using all Shimano SLX with 11 speed shifter, rear mech and chain. Front chain rings are 2 x SLX 38/28.
11 and 10 speed cranksets have slightly different chainring spacings to accommodate the difference in 11 and 10 speed chain widths. Front derailleurs have slightly different movement also.
You have a matching 10 speed front derailleur and crankset, so really the question is whether an 11 speed chain will work on a 10 speed front. I think from past answers I have seen here it will work OK.
It won't work well. It will be able to be adjusted such that it can physically move the chain from ring to ring, but it will be hard or impossible to get it and keep it adjusted so that there's no rub, no sluggish/hesitant shifting, and no propensity for chain drop.
Front derailer cages are matched to chain width, so in this case the cage will be wider than ideal. What tends to happen here is at the point where you have the inner cage adjusted close enough to the left side of the chain at its starting point for it to shift nicely up to the large ring, you'll then have too much gap on the other side of the chain once you're there, potentially causing derailment. You can try to use the high limit to mitigate this, but then it will shift badly if at all and over-stress the shifter mechanism (the cable will be statically stretched since the derailer wasn't able to move all the way, which puts a lot of force on the shifter mechanism when you try to release it, and accelerates shifter wear). And when you shift back down, the outer cage is further away from the chain than it should be, creating a clumsy shift.
Triples make the problem much worse. Doubles are still enough to force the qualty of the adjustment to be compromised. You can try bending around the derailer, but it doesn't tend to be really successful for this purpose, and then you're left with a mangled FD.
You can find lots of writing out there that downplays the significance of front derailer cage width. It's frequently parroted, and the degree to which it can be made to kinda sorta work enough for people to talk themselves into believing it's fine serves to reinforce the idea. But it's really not fine from a performance and probably enjoyment standpoint.