I have gout, can I take colchicine with indocin (indomethacin) together at the same time?

Yes! But this treats the attack only. You need to be on a uric-acid lowering agent. Allopurinol or uloric (if renal probs exist, and/or probenencid, usually combined with colchine, so i lower pill burden for my patients!
Yes. There is no interaction between Indomethacin and colchicine. They can be taken together. Both can cause upset stomach, however (from different mechanisms).

Related Questions

I have gout, can I take colchicine with indocin (indomethacin) together?

No. It is not recommended that you take the 2 drugs together. Read more...
Yes. I know of no drug-drug interaction between these 2 medications. You can always have a pharmacist check their computers. But the two medications listed work differently and hence there is no reason why they can't. Read more...