if its a woody material, chances are, that it won't decompose entirely during it's time in your pile, which means if you get it into the ground it could compete w/ your plants for nitrogen comsumption. Why not just put it back on your flower beds and let it decompose there? Mulch doesn't expire. It just dissappears eventually which is a good thing.

Why did you clean that mulch from that flower bed?
Why not use it for mulch someplace else?

Honestly, I thought it was ugly. I reworked the bed entirely. It had been neglected for a few years so I tilled the soil, added some new dirt, nutrients, etc. & put newspaper down for a weed barrier. Then I added some more dirt & did my flowers. I guess I could use it around the container bed where all my hot peppers are. Just put it around the pots. I hate to not use it--even tho I'm sure it looks attractive in a pile at the side of my house--so I thought it might do for some "browns" in the compost bin. I'm new to composting so I'm still trying to figure the science out. So far, tho, it seems to be doing well & things are breaking down in a short time & it has a nice, earthy smell.

the mulch has been composting right where it was, it's composting right now where it is, but the woody material takes longer to compost. it's really not something you want IN the ground. most will tell you that the only time wood is used it a compost pile is in the form of sawdust.

OK. I'll put it back into the flower bed with the containers. No wood chips for the compost; only sawdust & in small amounts. What else can I use to add more browns? I've about used up all the dead leaves around the yard. I put the coffee filters in as well as some shredded newspaper & papertowel/tp rolls (shredded).

Wood chips in the compost are just fine;
they won't decompose as quickly as paper & leaves, but it's perfectly ok to use compost with bits of undigested wood.

As sylvia has stated you can compost wood chips, they just can take a very long time to be digeted which is why most of use use wood chips for mulch. I asked why you removed them because even if you have the ugly red dyed wood chip mulch that can be covered with a more natural wood chip and hidden from view. No soil should be left bare and exposed to the ravages of the sun, wind, or rain, soil should always be covered with something such as a mulch or plants. Ma Nature always tries to grow plants on any bare soil and most of the time we call those plants "weeds".
Many things are browns and they are fairly readily available if we just look around. Leaves are easy because they are the most abundant source.