I heard IRS allows LIFO or HIFO method for crypto tax calculation (as oppose to FIFO),
Last In First Out is disallowed by many countries following the International Financial Reporting Standards [IFRS] but it is allowed under US Generally Accepted Accounting Principles [GAAP].
I have also read articles saying FIFO isn't allowed in the US but they are probably old. The 2019 IRS publication recognizes both LIFO and FIFO in identifying cost. Read
https://www.irs.gov/publications/p538I have not heard about the Highest In, First Out method but based on what I've read from my search, it is neither recognized under US GAAP or the IFRS.
but LIFO/HIFO methods require more thorough transaction records keeping?
Record keeping should depend on the method of valuation used. You can use all legal methods but how you keep your records should be the same.
1) Is that true? Does IRS even allow LIFO or HIFO for crypto tax?
Not HIFO as explained above.
2) If true, using API to import transaction documents from Coinbase to Koinly satisfy the record keeping requirement?
I believe so as there are no other more reliable records that you can present.
3) Also, does using either LIFO or HIFO increase the likelihood of audit than using FIFO?
Exclude HIFO.
The likelihood of getting audited by the IRS does not depend on the methods you used. It could be based on the amount you declared or the frequency of your filing. I don't know what other criteria tax bodies use but I really doubt it depends on cost valuation methods.
P.S.
My answers are guides only and not necessarily accurate. You should seek help from an accountant in your area.