CAN I USE CHEMICAL DYE ON HENNAED HAIR?
The short answer is yes, you can use chemical dye on hair treated with pure henna (compound henna is another story!) without more damage than chemical dye usually causes, but there are some things you should know, because the chemical dye won't behave the same way as it does on non-hennaed hair.
Using chemical dyes over hair colored with pure plant dyes won't destroy your hair structurally but will give unexpected results, usually much darker color than would normally be expected, because plant dyes don't “lift” easily. Chemical dyes may also fade faster than usual because henna makes your hair smoother and less porous so the chemical dyes won't attach as well, and often wash out with fewer shampoos.
Typically you can dye your hennaed hair darker with a chemical dye, but you can't go lighter by using a regular box dye. To attempt to go lighter with chemical dyes on hennaed hair, you'd need to do extensive lightening first and then attempt to color, but the heavy bleaching required to lift henna may make your hair unable to hold onto chemical dyes very well.
Caution: If you have used any indigo in your mix at all, it is not a good idea to try to go lighter chemically. Developer is mostly peroxide, and depending on what vol you're using, it can remove enough of all the other natural and plant pigments in the hair except the indigo, leaving you with green hair. For example if you use a high-lift blonde haircolor with 30 vol developer, or a highlighting kit with 40 vol, you will almost certainly see some green, and it is very likely that nothing plant or chemical will be able to remove or cover that green.
If the pure plant dyes you used contained only henna, cassia, or small amount of buxus and NO indigo, there is no worry about green tones showing up when using chemical dyes. If you used buxus multiple times to the point where your color was staying brown instead of fading back to red between buxus treatments, then you will likely encounter similar green issues if you try to bleach it.
If you have indigo (or lots of buxus, see above) in your hair and wish to chemically dye it equally dark, or darker, that should work fine. But if you try to bleach this hair first and fail, the residual green hair will not take chemical dyes well after that.